\(x^2-25=\) \(y\left(y+...">
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28 tháng 7 2017

\(x^2-25=y\left(y+6\right)\) (1)

\(\Leftrightarrow x^2-y^2-6y-25=0\)

\(\Leftrightarrow x^2-\left(y+3\right)^2=16\)

\(\Leftrightarrow\left(x-y-3\right)\left(x+y+3\right)=16\)

Xét các trường hợp, ta tìm được các no nguyên của pt (1).

\(x^2+x+6=y^2\) (2)

\(\Leftrightarrow4x^2+4x+24=4y^2\)

\(\Leftrightarrow\left(2x+1\right)^2-\left(2y^2\right)=-23\)

\(\Leftrightarrow\left(2x+1-2y\right)\left(2x+1+2y\right)=-23\)

Xét các trường hợp, ta tìm được các no nguyên của pt (2).

\(x^2+13y^2=100+6xy\) (3)

\(\Leftrightarrow x^2-6xy+9y^2+4y^2=100\)

\(\Leftrightarrow\left(x-3y\right)^2+\left(2y\right)^2=0^2+\left(\pm10\right)^2=\left(\pm6\right)^2+\left(\pm8\right)^2\)

Xét các trường hợp, ta tìm được các no nguyên của pt (3).

\(x^2-4x=169-5y^2\) (4)

\(\Leftrightarrow\left(x-2\right)^2+5y^2=173\)

Ta thấy:

\(5y^2\) luôn có chữ số tận cùng là 5 hoặc 0

=> Để thoả mãn pt (4), (x - 2)2 phải có chữ số tận cùng là 8 hoặc 3 (vô lý)

Vậy pt (4) vô n0.

\(x^2-x=6-y^2\) (5)

\(\Leftrightarrow4x^2-4x=24-4y^2\)

\(\Leftrightarrow\left(2x-1\right)^2+\left(2y\right)^2=25=\left(\pm25\right)^2+0^2=\left(\pm3\right)^2+\left(\pm4\right)^2\)

Xét các trường hợp, ta tìm được các no nguyên của pt (5).

28 tháng 7 2017

\(y^3=x^3+x^2+x+1\left(1\right)\)

Ta có:

\(y^3=x^3+\left(x+\dfrac{1}{2}\right)^2+\dfrac{3}{4}>x^3\)

\(\Rightarrow y>x\)

\(\Rightarrow y\ge x+1\)

\(\Rightarrow y^3\ge\left(x+1\right)^3\)

\(\Rightarrow x^3+x^2+x+1\ge x^3+3x^2+3x+1\)

\(\Leftrightarrow2x^2+2x\le0\)

\(\Leftrightarrow2x\left(x+1\right)\le0\)

\(\Rightarrow-1\le x\le0\) mà x là số nguyên

=> x = - 1 hoặc x = 0

(+) x = - 1

VT = 0

=> y = 0 ; x = - 1 (nhận)

(+) x = 0

VT = 1

=> y = 1 ; x = 0 (nhận)

Vậy pt (1) có nonguyên (x ; y) = (0 ; 1) ; (- 1 ; 0)

\(x^4+x^2+1=y^2\) (2)

(+)

\(\left(2\right)\Leftrightarrow y^2=x^4+2x^2+1-x^2\)

\(\Leftrightarrow y^2-\left(x^2+1\right)^2=x^2\)

(+)

\(\left(2\right)\Leftrightarrow x^4+4x^2+4-3x^2-3=y^2\)

\(\Leftrightarrow\left(x^2+2\right)^2-y^2=3\left(x^2+1\right)\)

Ta thấy:

Với mọi \(x\ne0\) thì \(\left(x^2+1\right)^2< y^2< \left(x^2+2\right)^2\) (vô lý)

=> x = 0

=> y = 1 (nhận)

Vậy pt (2) có nonguyên (x ; y) = (0 ; 1)

Bài 1: Thực hiện phép tính a, \(\dfrac{8}{\left(x^2+3\right)\left(x^2-1\right)}\)+\(\dfrac{2}{x^2+3}\)+\(\dfrac{1}{x+1}\) b, \(\dfrac{x+y}{2\left(x-y\right)}\)-\(\dfrac{x-y}{2\left(x+y\right)}\)+\(\dfrac{2y^2}{x^2-y^2}\) c, \(\dfrac{x-1}{x^3}\)-\(\dfrac{x+1}{x^3-x^2}\)+\(\dfrac{3}{x^3-2x^2+x}\) d, \(\dfrac{xy}{ab}\)+\(\dfrac{\left(x-a\right)\left(y-a\right)}{a\left(a-b\right)}\)-\(\dfrac{\left(x-b\right)\left(y-b\right)}{b\left(a-b\right)}\) e,...
Đọc tiếp

Bài 1: Thực hiện phép tính

a, \(\dfrac{8}{\left(x^2+3\right)\left(x^2-1\right)}\)+\(\dfrac{2}{x^2+3}\)+\(\dfrac{1}{x+1}\)

b, \(\dfrac{x+y}{2\left(x-y\right)}\)-\(\dfrac{x-y}{2\left(x+y\right)}\)+\(\dfrac{2y^2}{x^2-y^2}\)

c, \(\dfrac{x-1}{x^3}\)-\(\dfrac{x+1}{x^3-x^2}\)+\(\dfrac{3}{x^3-2x^2+x}\)

d, \(\dfrac{xy}{ab}\)+\(\dfrac{\left(x-a\right)\left(y-a\right)}{a\left(a-b\right)}\)-\(\dfrac{\left(x-b\right)\left(y-b\right)}{b\left(a-b\right)}\)

e, \(\dfrac{x^3}{x-1}\)-\(\dfrac{x^2}{x+1}\)-\(\dfrac{1}{x-1}\)+\(\dfrac{1}{x+1}\)

f, \(\dfrac{x^3+x^2-2x-20}{x^2-4}\)-\(\dfrac{5}{x+2}\)+\(\dfrac{3}{x-2}\)

g, \(\left\{\dfrac{x-y}{x+y}+\dfrac{x+y}{x-y}\right\}\).\(\left\{\dfrac{x^2+y^2}{2xy}\right\}\).\(\dfrac{xy}{x^2+y^2}\)

h, \(\dfrac{1}{\left(a-b\right)\left(b-c\right)}\)+\(\dfrac{1}{\left(b-c\right)\left(c-a\right)}\)+\(\dfrac{1}{\left(c-a\right)\left(a-b\right)}\)

i, \(\dfrac{\left[a^2-\left(b+c\right)^2\right]\left(a+b-c\right)}{\left(a+b+c\right)\left(a^2+c^2-2ac-b^2\right)}\)

k, \(\left[\dfrac{x^2-y^2}{xy}-\dfrac{1}{x+y}\left\{\dfrac{x^2}{y}-\dfrac{y^2}{x}\right\}\right]\):\(\dfrac{x-y}{x}\)

Bài 2: Rút gọn các phân thức:

a, \(\dfrac{25x^2-20x+4}{25x^2-4}\)

b, \(\dfrac{5x^2+10xy+5y^2}{3x^3+3y^3}\)

c, \(\dfrac{x^2-1}{x^3-x^2-x+1}\)

d, \(\dfrac{x^3+x^2-4x-4}{x^4-16}\)

e, \(\dfrac{4x^4-20x^3+13x^2+30x+9}{\left(4x^2-1\right)^2}\)

Bài 3: Rút gọn rồi tính giá trị các biểu thức:

a, \(\dfrac{a^2+b^2-c^2+2ab}{a^2-b^2+c^2+2ac}\) với a = 4, b = -5, c = 6

b, \(\dfrac{16x^2-40xy}{8x^2-24xy}\) với \(\dfrac{x}{y}\) = \(\dfrac{10}{3}\)

c, \(\dfrac{\dfrac{x^2+xy+y^2}{x+y}-\dfrac{x^2-xy+y^2}{x-y}}{x-y-\dfrac{x^2}{x+y}}\) với x = 9, y = 10

Bài 4: Tìm các giá trị nguyên của biến số x để biểu thức đã cho cũng có giá trị nguyên:

a, \(\dfrac{x^3-x^2+2}{x-1}\)

b, \(\dfrac{x^3-2x^2+4}{x-2}\)

c, \(\dfrac{2x^3+x^2+2x+2}{2x+1}\)

d, \(\dfrac{3x^3-7x^2+11x-1}{3x-1}\)

e, \(\dfrac{x^4-16}{x^4-4x^3+8x^2-16x+16}\)

2
8 tháng 12 2017

Giúp mình nhé mọi người ! leuleu

8 tháng 12 2017

\(1.\)

\(a.\)

\(\dfrac{8}{\left(x^2+3\right)\left(x^2-1\right)}+\dfrac{2}{x^2+3}+\dfrac{1}{x+1}\)

\(=\dfrac{8}{\left(x^2+3\right)\left(x^2-1\right)}+\dfrac{2\left(x^2-1\right)}{\left(x^2+3\right)\left(x^2-1\right)}+\dfrac{1\left(x-1\right)\left(x^2+3\right)}{\left(x^2-1\right)\left(x^2+3\right)}\)

\(=\dfrac{8}{\left(x^2+3\right)\left(x^2-1\right)}+\dfrac{2x^2-2}{\left(x^2+3\right)\left(x^2-1\right)}+\dfrac{x^3-x^2+3x-3}{\left(x^2-1\right)\left(x^2+3\right)}\)

\(=\dfrac{8+2x^2-2+x^3-x^2+3x-3}{\left(x^2+3\right)\left(x^2-1\right)}\)

\(=\dfrac{x^3+x^2+3x+3}{\left(x^2+3\right)\left(x^2-1\right)}\)

\(=\dfrac{x^2\left(x+1\right)+3\left(x+1\right)}{\left(x^2+3\right)\left(x^2-1\right)}\)

\(=\dfrac{\left(x^2+3\right)\left(x+1\right)}{\left(x^2+3\right)\left(x^2-1\right)}\)

\(=x-1\)

\(b.\)

\(\dfrac{x+y}{2\left(x-y\right)}-\dfrac{x-y}{2\left(x+y\right)}+\dfrac{2y^2}{x^2-y^2}\)

\(=\dfrac{x+y}{2\left(x-y\right)}-\dfrac{x-y}{2\left(x+y\right)}+\dfrac{2y^2}{\left(x-y\right)\left(x+y\right)}\)

\(=\dfrac{\left(x+y\right)^2}{2\left(x^2-y^2\right)}-\dfrac{\left(x-y\right)^2}{2\left(x^2-y^2\right)}+\dfrac{4y^2}{2\left(x^2-y^2\right)}\)

\(=\dfrac{x^2+2xy+y^2}{2\left(x^2-y^2\right)}-\dfrac{x^2-2xy+y^2}{2\left(x^2-y^2\right)}+\dfrac{4y^2}{2\left(x^2-y^2\right)}\)

\(=\dfrac{x^2+2xy+y^2-x^2+2xy-y^2+4y^2}{2\left(x^2-y^2\right)}\)

\(=\dfrac{4xy+4y^2}{2\left(x^2-y^2\right)}\)

\(=\dfrac{4y\left(x+y\right)}{2\left(x^2-y^2\right)}\)

\(=\dfrac{2y}{\left(x-y\right)}\)

Tương tự các câu còn lại

AH
Akai Haruma
Giáo viên
24 tháng 11 2018

a)

\(\frac{x^2-16}{4x-x^2}=\frac{x^2-4^2}{x(4-x)}=\frac{(x-4)(x+4)}{x(4-x)}=\frac{x+4}{-x}\)

b) \(\frac{x^2+4x+3}{2x+6}=\frac{x^2+x+3x+3}{2(x+3)}=\frac{x(x+1)+3(x+1)}{2(x+3)}=\frac{(x+1)(x+3)}{2(x+3)}=\frac{x+1}{2}\)

c)

\(\frac{15x(x+y)^3}{5y(x+y)^2}=\frac{5.3.x(x+y)^2.(x+y)}{5y(x+y)^2}=\frac{3x(x+y)}{y}\)

d) \(\frac{5(x-y)-3(y-x)}{10(x-y)}=\frac{5(x-y)+3(x-y)}{10(x-y)}=\frac{8(x-y)}{10(x-y)}=\frac{8}{10}=\frac{4}{5}\)

AH
Akai Haruma
Giáo viên
24 tháng 11 2018

e) \(\frac{2x+2y+5x+5y}{2x+2y-5x-5y}=\frac{7x+7y}{-3x-3y}=\frac{7(x+y)}{-3(x+y)}=\frac{-7}{3}\)

f) \(\frac{x^2-xy}{3xy-3y^2}=\frac{x(x-y)}{3y(x-y)}=\frac{x}{3y}\)

g) \(\frac{2ax^2-4ax+2a}{5b-5bx^2}=\frac{2a(x^2-2x+1)}{5b(1-x^2)}=\frac{2a(x-1)^2}{5b(1-x)(1+x)}\)

\(=\frac{2a(x-1)}{5b(-1)(x+1)}=\frac{2a(1-x)}{5b(x+1)}\)

10 tháng 11 2017

Câu 1:

\(\text{a) }\dfrac{x^2-xy}{3xy-3y^2}=\dfrac{x\left(x-y\right)}{3y\left(x-y\right)}=\dfrac{x}{3y}\)

\(\text{b) }\dfrac{2ax^2-4ax+2a}{5b-5bx^2}\\ =\dfrac{2a\left(x^2-2x+1\right)}{5b\left(1-x^2\right)}\\ =\dfrac{2a\left(x-1\right)^2}{5b\left(1-x\right)\left(1+x\right)}\\ =-\dfrac{2a\left(x-1\right)^2}{5b\left(x-1\right)\left(1+x\right)}\\ =-\dfrac{2a\left(x-1\right)}{5b\left(x+1\right)}\\ =-\dfrac{2ax-2a}{5bx+5b}\)

\(\text{c) }\dfrac{4x^2-4xy}{5x^3-5x^2y}=\dfrac{4x\left(x-y\right)}{5x^2\left(x-y\right)}=\dfrac{4}{5x}\)

\(\text{d) }\dfrac{\left(x+y\right)^2-z^2}{x+y+z}=\dfrac{\left(x+y+z\right)\left(x+y-z\right)}{x+y+z}=x+y-z\)

\(\text{e) }\dfrac{x^6+2x^3y^3+y^6}{x^7-xy^6}\\ =\dfrac{\left(x^3+y^3\right)^2}{x\left(x^6-y^6\right)}\\ =\dfrac{\left(x^3+y^3\right)^2}{x\left(x^3-y^3\right)\left(x+y\right)^3}\\ =\dfrac{x^3+y^3}{x\left(x^3-y^3\right)}\\ =\dfrac{x^3+y^3}{x^4-xy^3}\)

10 tháng 11 2017

Câu 3:

\(\text{ a) }\dfrac{\left(a+b\right)^2-c^2}{a+b+c}=\dfrac{\left(a+b+c\right)\left(a+b-c\right)}{a+b+c}=a+b-c\)

\(\text{b) }\dfrac{a^2+b^2-c^2+2ab}{a^2-b^2+c^2+2ac}\\ =\dfrac{\left(a^2+2ab+b^2\right)-c^2}{\left(a^2+2ac+c^2\right)-b^2}\\ =\dfrac{\left(a+b\right)^2-c^2}{\left(a+c\right)^2-b^2}\\ =\dfrac{\left(a+b+c\right)\left(a+b-c\right)}{\left(a+c+b\right)\left(a+c-b\right)}\\ =\dfrac{a+b-c}{a-b+c}\)

\(\text{c) }\dfrac{2x^3-7x^2-12x+45}{3x^3-19x^2+33x-9}\\ =\dfrac{2x^3-x^2-6x^2+3x-15x+45}{3x^3-10x^2-9x^2+3x+30x-9}\\ =\dfrac{\left(2x^3-x^2-15x\right)-\left(6x^2-3x-45\right)}{\left(3x^3-10x^2+3x\right)-\left(9x^2-30x+9\right)}\\ =\dfrac{x\left(2x^2-x-15\right)-3\left(2x^2-x-15\right)}{x\left(3x^2-10x+3\right)-3\left(3x^2-10x+3\right)}\\ =\dfrac{\left(x-3\right)\left(2x^2-x-15\right)}{\left(x-3\right)\left(3x^2-10x+3\right)}\\ =\dfrac{\left(x-3\right)\left(2x^2-6x+5x-15\right)}{\left(x-3\right)\left(3x^2-9x-x+3\right)}\\ =\dfrac{\left(x-3\right)\left[\left(2x^2-6x\right)+\left(5x-15\right)\right]}{\left(x-3\right)\left[\left(3x^2-9x\right)-\left(x-3\right)\right]}\\ =\dfrac{\left(x-3\right)\left[x\left(x-3\right)+5\left(x-3\right)\right]}{\left(x-3\right)\left[3x\left(x-3\right)-\left(x-3\right)\right]}\\ =\dfrac{\left(x-3\right)\left(x-3\right)\left(x+5\right)}{\left(x-3\right)\left(x-3\right)\left(3x-1\right)}\\ =\dfrac{x+5}{3x-1}\)

7 tháng 5 2018

nhân cả 2 vế với 2 rồi bunhia

6 tháng 4 2018

câu c là \(\dfrac{1}{2}\)(x+y+z) nhé, mih chép nhầm

AH
Akai Haruma
Giáo viên
29 tháng 11 2018

Bài 1:

Đặt \(\left(\frac{x}{y}; \frac{y}{z}; \frac{z}{x}\right)=(a,b,c)\Rightarrow abc=1\)

Khi đó:

\(A^2+B^2+C^2-ABC=(b+\frac{1}{b})^2+(c+\frac{1}{c})^2+(a+\frac{1}{a})^2-(a+\frac{1}{a})(b+\frac{1}{b})(c+\frac{1}{c})\)

\(=b^2+\frac{1}{b^2}+2+c^2+\frac{1}{c^2}+2+a^2+\frac{1}{a^2}+2-(ab+\frac{a}{b}+\frac{b}{a}+\frac{1}{ab})(c+\frac{1}{c})\)

\(a^2+b^2+c^2+(\frac{1}{a^2}+\frac{1}{b^2}+\frac{1}{c^2})+6-[abc+\left(\frac{ab}{c}+\frac{bc}{a}+\frac{ca}{b}\right)+\left(\frac{a}{bc}+\frac{b}{ac}+\frac{c}{ab}\right)+\frac{1}{abc}]\)

\(=a^2+b^2+c^2+\frac{1}{a^2}+\frac{1}{b^2}+\frac{1}{c^2}+6-[1+\left(\frac{abc}{c^2}+\frac{abc}{a^2}+\frac{abc}{b^2}\right)+\left(\frac{a^2}{abc}+\frac{b^2}{abc}+\frac{c^2}{abc}\right)+1]\)

\(=a^2+b^2+c^2+\frac{1}{a^2}+\frac{1}{b^2}+\frac{1}{c^2}+6-[1+(\frac{1}{c^2}+\frac{1}{b^2}+\frac{1}{a^2})+(a^2+b^2+c^2)+1]\)

\(=4\)

AH
Akai Haruma
Giáo viên
29 tháng 11 2018

Câu 2:

Ta có:

\(xy+yz+xz+2xyz=\frac{ab}{(b+c)(c+a)}+\frac{bc}{(c+a)(a+b)}+\frac{ac}{(b+c)(a+b)}+\frac{2abc}{(a+b)(b+c)(c+a)}\)

\(=\frac{ab(a+b)}{(a+b)(b+c)(c+a)}+\frac{bc(b+c)}{(a+b)(b+c)(c+a)}+\frac{ac(a+c)}{(a+b)(b+c)(c+a)}+\frac{2abc}{(a+b)(b+c)(c+a)}\)

\(=\frac{ab(a+b)+bc(b+c)+ca(c+a)+2abc}{(a+b)(b+c)(c+a)}\)

\(=\frac{ab(a+b+c)+bc(b+c+a)+ca(c+a)}{(a+b)(b+c)(c+a)}\)

\(=\frac{(a+b+c)(ab+bc)+ac(a+c)}{(a+b)(b+c)(c+a)}=\frac{(c+a)b(a+b+c)+ac(a+c)}{(a+b)(b+c)(c+a)}\)

\(=\frac{(a+c)[b(a+b+c)+ac]}{(a+b)(b+c)(c+a)}=\frac{(a+c)[b(a+b)+c(a+b)]}{(a+b)(b+c)(c+a)}\)

\(=\frac{(a+c)(b+c)(a+b)}{(a+b)(b+c)(c+a)}=1\)

1, Thực hiện phép tính : a, \(\dfrac{2x+4}{10}\) + \(\dfrac{2-x}{15}\) b, \(\dfrac{3x}{10}\) + \(\dfrac{2x-1}{15}\) + \(\dfrac{2-x}{20}\) c, \(\dfrac{x+1}{2x-2}\) + \(\dfrac{x^2+3}{2-2x^2}\) d, \(\dfrac{1-2x}{2x}\) + \(\dfrac{2x}{2x-1}\) + \(\dfrac{1}{2x-4x^2}\) e, \(\dfrac{x}{xy-y^2}\) + \(\dfrac{2x-y}{xy-x^2}\) f, \(\dfrac{x^2}{x^2-4x}\) + \(\dfrac{6}{6-3x}\) +\(\dfrac{1}{x+2}\) g, \(\dfrac{2x^2-10xy}{2xy}\) + \(\dfrac{5y-x}{y}\) + \(\dfrac{x+2y}{x}\) h, \(\dfrac{2}{x+y}\)...
Đọc tiếp

1, Thực hiện phép tính :

a, \(\dfrac{2x+4}{10}\) + \(\dfrac{2-x}{15}\)

b, \(\dfrac{3x}{10}\) + \(\dfrac{2x-1}{15}\) + \(\dfrac{2-x}{20}\)

c, \(\dfrac{x+1}{2x-2}\) + \(\dfrac{x^2+3}{2-2x^2}\)

d, \(\dfrac{1-2x}{2x}\) + \(\dfrac{2x}{2x-1}\) + \(\dfrac{1}{2x-4x^2}\)

e, \(\dfrac{x}{xy-y^2}\) + \(\dfrac{2x-y}{xy-x^2}\)

f, \(\dfrac{x^2}{x^2-4x}\) + \(\dfrac{6}{6-3x}\) +\(\dfrac{1}{x+2}\)

g, \(\dfrac{2x^2-10xy}{2xy}\) + \(\dfrac{5y-x}{y}\) + \(\dfrac{x+2y}{x}\)

h, \(\dfrac{2}{x+y}\) +\(\dfrac{1}{x-y}\) + \(\dfrac{-3x}{x^2-y^2}\)

i, x+y+ \(\dfrac{x^2+y^2}{x+y}\)

2, Thực hiện phép tính :

a, \(\dfrac{2x}{x^2+2xy}\) + \(\dfrac{y}{xy-2y^2}\)+ \(\dfrac{4}{x^2-4y^2}\)

b, \(\dfrac{1}{x-y}\) + \(\dfrac{3xy}{y^3-x^3}\) + \(\dfrac{x-y}{x^2+xy+y^2}\)

c, \(\dfrac{2x+y}{2x^2-xy}\) + \(\dfrac{16x}{y^2-4x^2}\) + \(\dfrac{2x-y}{2x^2+xy}\)

d, \(\dfrac{1}{1-x}\) +\(\dfrac{1}{1+x}\) + \(\dfrac{2}{1+x^2}\) + \(\dfrac{4}{1+x^4}\) + \(\dfrac{8}{1+x^8}\)+ \(\dfrac{16}{1+x^{16}}\)

1
13 tháng 11 2017

Bài 2 .

a) \(\dfrac{2x}{x^2+2xy}+\dfrac{y}{xy-2y^2}+\dfrac{4}{x^2-4y^2}\)

\(=\dfrac{2x}{x\left(x+2y\right)}+\dfrac{y}{y\left(x-2y\right)}+\dfrac{4}{\left(x-2y\right)\left(x+2y\right)}\)

\(=\dfrac{2xy\left(x-2y\right)+xy\left(x+2y\right)+4xy}{xy\left(x+2y\right)\left(x-2y\right)}\)

\(=\dfrac{2x^2y-2xy^2+x^2y+2xy^2+4xy}{xy\left(x+2y\right)\left(x-2y\right)}\)

\(=\dfrac{3x^2y+4xy}{xy\left(x+2y\right)\left(x-2y\right)}\)

b) Sai đề hay sao ý

c) \(\dfrac{2x+y}{2x^2-xy}+\dfrac{16x}{y^2-4x^2}+\dfrac{2x-y}{2x^2+xy}\)

\(=\dfrac{2x+y}{x\left(2x-y\right)}+\dfrac{-16x}{\left(2x-y\right)\left(2x+y\right)}+\dfrac{2x-y}{x\left(2x+y\right)}\)

\(=\dfrac{\left(2x+y\right)^2-16x^2+\left(2x-y\right)^2}{x\left(2x-y\right)\left(2x+y\right)}\)

\(=\dfrac{4x^2+4xy+y^2-16x^2+4x^2-4xy+y^2}{x\left(2x-y\right)\left(2x+y\right)}\)

\(=\dfrac{-8x^2}{x\left(2x-y\right)\left(2x+y\right)}\)

d) \(\dfrac{1}{1-x}+\dfrac{1}{1+x}+\dfrac{2}{1+x^2}+\dfrac{4}{1+x^4}+\dfrac{8}{1+x^8}+\dfrac{16}{1+x^{16}}\)

\(=\dfrac{2}{1-x^2}+\dfrac{2}{1+x^2}+\dfrac{4}{1+x^4}+\dfrac{8}{1+x^8}+\dfrac{16}{1+x^{16}}\)

\(=\dfrac{4}{1-x^4}+\dfrac{4}{1+x^4}+\dfrac{8}{1+x^8}+\dfrac{16}{1+x^{16}}\)

.....

\(=\dfrac{16}{1-x^{16}}+\dfrac{16}{1+x^{16}}\)

\(=\dfrac{32}{1-x^{32}}\)

15 tháng 11 2017

2)

a) \(\dfrac{1}{x}.\dfrac{6x}{y}\)

\(=\dfrac{6x}{xy}\)

\(=\dfrac{6}{y}\)

b) \(\dfrac{2x^2}{y}.3xy^2\)

\(=\dfrac{2x^2.3xy^2}{y}\)

\(=\dfrac{6x^3y^2}{y}\)

\(=6x^3y\)

c) \(\dfrac{15x}{7y^3}.\dfrac{2y^2}{x^2}\)

\(=\dfrac{15x.2y^2}{7y^3.x^2}\)

\(=\dfrac{30xy^2}{7x^2y^3}\)

\(=\dfrac{30}{7xy}\)

d) \(\dfrac{2x^2}{x-y}.\dfrac{y}{5x^3}\)

\(=\dfrac{2x^2.y}{\left(x-y\right).5x^3}\)

\(=\dfrac{2y}{5x\left(x-y\right)}\)

7 tháng 11 2017

1)

a) \(\dfrac{5x}{10}=\dfrac{x}{2}\)

b) \(\dfrac{4xy}{2y}=2x\left(y\ne0\right)\)

c) \(\dfrac{21x^2y^3}{6xy}=\dfrac{7xy^2}{2}\left(xy\ne0\right)\)

d) \(\dfrac{2x+2y}{4}=\dfrac{2\left(x+y\right)}{4}=\dfrac{x+y}{2}\)

e) \(\dfrac{5x-5y}{3x-3y}=\dfrac{5\left(x-y\right)}{3\left(x-y\right)}=\dfrac{5}{3}\left(x\ne y\right)\)

f) \(\dfrac{-15x\left(x-y\right)}{3\left(y-x\right)}=-5x\dfrac{x-y}{y-x}=-5x\dfrac{x-y}{-\left(x-y\right)}\)

\(=-5x.\left(-1\right)=5x\left(x\ne y\right)\)

2)

a) Nhớ ghi ĐK vào nhá, lười quá :V\(\dfrac{x^2-16}{4x-x^2}=-\dfrac{\left(x-4\right)\left(x+4\right)}{x^2-4x}=\dfrac{\left(x-4\right)\left(x+4\right)}{x\left(x-4\right)}=\dfrac{x+4}{x}\)

b) \(\dfrac{x^2+4x+3}{2x+6}=\dfrac{x^2+3x+x+3}{2\left(x+3\right)}=\dfrac{x\left(x+3\right)+\left(x+3\right)}{2\left(x+3\right)}\)

\(=\dfrac{\left(x+3\right)\left(x+1\right)}{2\left(x+3\right)}=\dfrac{x+1}{2}\)

c) \(\dfrac{15x\left(x+3\right)^3}{5y\left(x+y\right)^2}=\dfrac{3x\left(x+3\right)^3}{y\left(x+y\right)^2}\) ( câu này có gì đó sai sai )

d) \(\dfrac{5\left(x-y\right)-3\left(y-x\right)}{10\left(x-y\right)}=\dfrac{5\left(x-y\right)+3\left(x-y\right)}{10\left(x-y\right)}\)

\(=\dfrac{8\left(x-y\right)}{10\left(x-y\right)}=\dfrac{8}{10}=\dfrac{4}{5}\)

e) \(\dfrac{2x+2y+5x+5y}{2x+2y-5x-5y}=\dfrac{2\left(x+y\right)+5\left(x+y\right)}{2\left(x+y\right)-5\left(x+y\right)}\)

\(=\dfrac{7\left(x+y\right)}{-3\left(x+y\right)}=-\dfrac{7}{3}\)

18 tháng 11 2017

\(1.\text{ }\text{ }\text{ }\dfrac{\left(x^2+2\right)^2-4x^2}{y\left(x^2+2\right)-2xy-\left(x-1\right)^2-1}\\ =\dfrac{\left(x^2+2-2x\right)\left(x^2+2+2x\right)}{x^2y+2y-2xy-x^2+2x-1-1}\\ =\dfrac{\left(x^2+2-2x\right)\left(x^2+2+2x\right)}{\left(x^2y-x^2\right)-\left(2xy-2x\right)+\left(2y-2\right)}\\ =\dfrac{\left(x^2+2-2x\right)\left(x^2+2+2x\right)}{x^2\left(y-1\right)-2x\left(y-1\right)+2\left(y-1\right)}\\ =\dfrac{\left(x^2+2-2x\right)\left(x^2+2+2x\right)}{\left(x^2-2x+2\right)\left(y-1\right)}\\ =\dfrac{x^2+2x+2}{y-1}\)

\(2.\text{ }\text{ }\text{ }\text{ }\dfrac{x^2+5x+6}{x^2+3x+2}\\ =\dfrac{x^2+3x+2x+6}{x^2+2x+x+2}\\ =\dfrac{\left(x^2+3x\right)+\left(2x+6\right)}{\left(x^2+2x\right)+\left(x+2\right)}\\ =\dfrac{x\left(x+3\right)+2\left(x+3\right)}{x\left(x+2\right)+\left(x+2\right)}\\ =\dfrac{\left(x+2\right)\left(x+3\right)}{\left(x+2\right)\left(x+1\right)}\\ =\dfrac{x+3}{x+1}\)

\(3.\text{ }\text{ }\text{ }\dfrac{x^2+y^2-z^2-2zt+2xy-t^2}{x^2-y^2+z^2-2yt+2xz-t^2}\text{ ( Chữa đề ) }\\ =\dfrac{\left(x^2+2xy+y^2\right)-\left(z^2+2zt+t^2\right)}{\left(x^2+2xz+z^2\right)-\left(y^2+2yt+t^2\right)}\\ =\dfrac{\left(x+y\right)^2-\left(z+t\right)^2}{\left(x+z\right)^2-\left(y+t\right)^2}\\ =\dfrac{\left(x+y+z+t\right)\left(x+y-z-t\right)}{\left(x+z+y+t\right)\left(x+z-y-t\right)}\\ =\dfrac{x+y-z-t}{x+z-y-t}\)

\(4.\text{ }\text{ }\text{ }\dfrac{\left(n+1\right)!}{\left(n+1\right)!+\left(n+2\right)!}=\dfrac{\left(n+1\right)!}{\left(n+1\right)!\left(1+n+2\right)}=\dfrac{1}{n+3}\)

\(5.\text{ }\text{ }\text{ }\dfrac{x^2+5x+4}{x^2-1}\\ =\dfrac{x^2+x+4x+4}{\left(x+1\right)\left(x-1\right)}\\ =\dfrac{\left(x^2+x\right)+\left(4x+4\right)}{\left(x+1\right)\left(x-1\right)}\\ =\dfrac{x\left(x+1\right)+4\left(x+1\right)}{\left(x+1\right)\left(x-1\right)}\\ =\dfrac{\left(x+1\right)\left(x+4\right)}{\left(x+1\right)\left(x-1\right)}\\ =\dfrac{x+4}{x-1}\)

\(6.\text{ }\text{ }\text{ }\dfrac{x^2-3x}{2x^2-7x+3}\\ =\dfrac{x\left(x-3\right)}{2x^2-6x-x+3}\\ =\dfrac{x\left(x-3\right)}{\left(2x^2-6x\right)-\left(x-3\right)}\\ =\dfrac{x\left(x-3\right)}{2x\left(x-3\right)-\left(x-3\right)}\\ =\dfrac{x\left(x-3\right)}{\left(2x-1\right)\left(x-3\right)}\\ =\dfrac{x}{2x-1}\)