\(\dfrac{x+3}{x-2}\) + \(\dfrac{4+x}{...">
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20 tháng 12 2018

a.

\(\dfrac{x+3}{x-2}+\dfrac{4+x}{2-x}\\ =\dfrac{x+3}{x-2}-\dfrac{4+x}{x-2}\\ =\dfrac{x+3-4-x}{x-2}\\ =-\dfrac{1}{x-2}\)

b. \(\dfrac{x+1}{2x+6}+\dfrac{2x+3}{x^2+3x}\)

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

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

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

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

\(=\dfrac{x+2}{2x}\)

c. \(\dfrac{3}{2x+6}-\dfrac{x-6}{2x^2+6x}\)

\(=\dfrac{3}{2\left(x+3\right)}-\dfrac{x-6}{2x\left(x+3\right)}\)

\(=\dfrac{3x}{2x\left(x+3\right)}-\dfrac{x-6}{2x\left(x+3\right)}\)

\(=\dfrac{3x-x+6}{2x\left(x+3\right)}=\dfrac{2x+6}{2x\left(x+3\right)}=\dfrac{2\left(x+3\right)}{2x\left(x+3\right)}\)

\(=\dfrac{1}{x}\)

d. \(\dfrac{2x+6}{3x^2-x}:\dfrac{x^2+3x}{1-3x}\)

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

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

\(=-\dfrac{2}{x^2}\)

20 tháng 12 2018

bị mỏi tay nhỉ

14 tháng 12 2018

a) \(\dfrac{x}{x-3}+\dfrac{9-6x}{x^2-3x}=\dfrac{x^2}{x\left(x-3\right)}+\dfrac{9-6x}{x\left(x-3\right)}=\dfrac{x^2-6x+9}{x\left(x-3\right)}=\dfrac{\left(x-3\right)^2}{x\left(x-3\right)}=\dfrac{x-3}{x}\)

14 tháng 12 2018

thanks

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

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

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

10 tháng 12 2018

1.

a) \(x\left(x+4\right)+x+4=0\)

\(\Leftrightarrow\left(x+1\right)\left(x+4\right)=0\)

\(\Leftrightarrow\left[{}\begin{matrix}x+4=0\\x+1=0\end{matrix}\right.\Rightarrow\left[{}\begin{matrix}x=-4\\x=-1\end{matrix}\right.\)

b) \(x\left(x-3\right)+2x-6=0\)

\(\Leftrightarrow\left(x+2\right)\left(x-3\right)=0\)

\(\Leftrightarrow\left[{}\begin{matrix}x+2=0\\x-3=0\end{matrix}\right.\Rightarrow\left[{}\begin{matrix}x=-2\\x=3\end{matrix}\right.\)

10 tháng 12 2018

Bài 1:

a, \(x\left(x+4\right)+x+4=0\)

\(\Leftrightarrow x\left(x+4\right)+\left(x+4\right)=0\)

\(\Leftrightarrow\left(x+4\right)\left(x+1\right)=0\)

\(\Leftrightarrow\left[{}\begin{matrix}x+4=0\\x+1=0\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=-4\\x=-1\end{matrix}\right.\)

Vậy \(x=-4\) hoặc \(x=-1\)

b, \(x\left(x-3\right)+2x-6=0\)

\(\Leftrightarrow x\left(x-3\right)+2\left(x-3\right)=0\)

\(\Leftrightarrow\left(x-3\right)\left(x+2\right)=0\)

\(\Leftrightarrow\left[{}\begin{matrix}x-3=0\\x+2=0\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=3\\x=-2\end{matrix}\right.\)

Vậy \(x=3\) hoặc \(x=-2\)

1 tháng 12 2017

a) \(\dfrac{3}{2x+6}-\dfrac{x-6}{2x^2+6x}\)

\(=\dfrac{3}{2\left(x+3\right)}-\dfrac{x-6}{2x\left(x+3\right)}\) MTC: \(2x\left(x+3\right)\)

\(=\dfrac{3x}{2x\left(x+3\right)}-\dfrac{x-6}{2x\left(x+3\right)}\)

\(=\dfrac{3x-\left(x-6\right)}{2x\left(x+3\right)}\)

\(=\dfrac{3x-x+6}{2x\left(x+3\right)}\)

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

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

\(=\dfrac{1}{x}\)

b) \(\dfrac{4}{x+2}+\dfrac{2}{x-2}+\dfrac{5x+6}{4-x^2}\)

\(=\dfrac{4}{x+2}+\dfrac{2}{x-2}-\dfrac{5x+6}{x^2-4}\)

\(=\dfrac{4}{x+2}+\dfrac{2}{x-2}-\dfrac{5x+6}{\left(x-2\right)\left(x+2\right)}\) MTC: \(\left(x-2\right)\left(x+2\right)\)

\(=\dfrac{4\left(x-2\right)}{\left(x-2\right)\left(x+2\right)}+\dfrac{2\left(x+2\right)}{\left(x-2\right)\left(x+2\right)}-\dfrac{5x+6}{\left(x-2\right)\left(x+2\right)}\)

\(=\dfrac{4\left(x-2\right)+2\left(x+2\right)-\left(5x+6\right)}{\left(x-2\right)\left(x+2\right)}\)

\(=\dfrac{4x-8+2x+4-5x-6}{\left(x-2\right)\left(x+2\right)}\)

\(=\dfrac{x-10}{\left(x-2\right)\left(x+2\right)}\)

1 tháng 12 2017

c) \(\dfrac{1-3x}{2x}+\dfrac{3x-2}{2x-1}+\dfrac{3x-2}{2x-4x^2}\)

\(=\dfrac{1-3x}{2x}+\dfrac{3x-2}{2x-1}-\dfrac{3x-2}{4x^2-2x}\)

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

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

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

\(=\dfrac{2x-1-6x^2+3x+6x^2-4x-3x+2}{2x\left(2x-1\right)}\)

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

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

\(=\dfrac{-1}{2x}\)

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

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

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

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

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

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

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

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

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

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

.....

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

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

7 tháng 1 2018

mn ơi đề bài là rút gọn phân thức.Mk cần gấp

a: \(=\dfrac{2x^2}{x^2-1}+\dfrac{6}{x-3}-\dfrac{2x-6}{\left(x-3\right)\left(x^2-1\right)}\)

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

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

b: \(=\dfrac{x+3}{x\left(x-6\right)}-\dfrac{x+9}{\left(x-6\right)\left(x+4\right)}+1\)

\(=\dfrac{\left(x+3\right)\left(x+4\right)-x\left(x+9\right)+x\left(x-6\right)\left(x+4\right)}{x\left(x-6\right)\left(x+4\right)}\)

\(=\dfrac{x^2+7x+12-x^2-9x+x\left(x^2-2x-24\right)}{x\left(x-6\right)\left(x+4\right)}\)

\(=\dfrac{-2x+12+x^3-2x^2-24x}{x\left(x-6\right)\left(x+4\right)}\)

\(=\dfrac{x^3-2x^2-26x+12}{x\left(x-6\right)\left(x+4\right)}\)

\(=\dfrac{x^3-6x^2+4x^2-24x-2x+12}{x\left(x-6\right)\left(x+4\right)}\)

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

9 tháng 5 2018

Mấy này bạn quy đồng lên cùng mẫu xong khử mẫu rồi giải. Dễ mà.