a)\(\dfrac{3}{2y+4}-\dfrac{1}{3y+6}\) b)\(\dfrac{1}{2x-3}-\dfrac{1}{2x+3}\)

K

Khách

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Mua vip

HK

Huỳnh Kim Bảo

27 tháng 11 2018

a)\(\dfrac{3}{2y+4}-\dfrac{1}{3y+6}\)

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

c)\(\dfrac{1}{xy-x^2}-\dfrac{1}{y^2-xy}\)

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

3

LK

lâm khánh đại

27 tháng 11 2018

Phép trừ các phân thức đại số

LK

lâm khánh đại

27 tháng 11 2018

Phép trừ các phân thức đại số

Các câu hỏi dưới đây có thể giống với câu hỏi trên

AP

Annh Phươngg

1 tháng 12 2018

3. Làm tính trừ các phân thức sau:

a) \(\dfrac{3}{2y+4}-\dfrac{1}{3y+6}\)

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

c) \(\dfrac{1}{xy-x^2}-\dfrac{1}{y^2-xy}\)

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

2

TT

Trần Thanh Phương

3 tháng 12 2018

ĐKXĐ bạn tự xét nha ^^

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

\(=\dfrac{9}{6\left(y+2\right)}-\dfrac{2}{6\left(y+2\right)}=\dfrac{9-2}{6\left(y+2\right)}\)

\(=\dfrac{7}{6\left(y+2\right)}\)

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

\(=\dfrac{2x+3-2x+3}{\left(2x-3\right)\left(2x+3\right)}=\dfrac{6}{4x^2-9}\)

c) \(\dfrac{1}{xy-x^2}-\dfrac{1}{y^2-xy}=\dfrac{1}{x\left(y-x\right)}-\dfrac{1}{y\left(y-x\right)}\)

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

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

d) \(\dfrac{x+1}{x+4}-\dfrac{x^2-4}{x^2-16}=\dfrac{\left(x+1\right)\left(x-4\right)}{\left(x+4\right)\left(x-4\right)}-\dfrac{\left(x-2\right)\left(x+2\right)}{\left(x+4\right)\left(x-4\right)}\)

\(=\dfrac{x^2-3x-4-x^2+4}{\left(x+4\right)\left(x-4\right)}=\dfrac{-3x}{x^2-16}\)

NT

NGUYỄN THỊ QUỲNH

2 tháng 12 2018

a,

QN

Quỳnh Như

7 tháng 8 2017

Thực hiện các phép tính với các phân thức sau: a) \(\dfrac{4a^2-3a+5}{a^3-1}-\dfrac{1-2a}{a^2+a+1}-\dfrac{6}{a-1}\) b) \(\dfrac{5}{a+1}-\dfrac{10}{a-\left(a^2+1\right)}-\dfrac{15}{a^3+1}\) c) \(\dfrac{2x}{x^2+2xy}+\dfrac{y}{xy-2y^2}+\dfrac{4}{x^2-4y^2}\) d) \(\dfrac{1}{x-y}+\dfrac{3xy}{y^3-x^3}+\dfrac{x-y}{x^2+xy+y^2}\) e) \(\dfrac{2x+y}{2x^2-xy}+\dfrac{16x}{y^2-4x^2}+\dfrac{2x-y}{2x^2+xy}\) f)...

1

NL

Nguyễn Lê Phước Thịnh

24 tháng 5 2022

a: \(=\dfrac{4a^2-3a+5}{\left(a-1\right)\left(a^2+a+1\right)}+\dfrac{\left(2a-1\right)\left(a-1\right)}{\left(a-1\right)\left(a^2+a+1\right)}-\dfrac{6a^2+6a+1}{\left(a-1\right)\left(a^2+a+1\right)}\)

\(=\dfrac{4a^2-3a+5+2a^2-3a+1-6a^2-6a-6}{\left(a-1\right)\left(a^2+a+1\right)}\)

\(=\dfrac{-12a}{\left(a-1\right)\left(a^2+a+1\right)}\)

b: \(=\dfrac{5}{a+1}+\dfrac{10}{a^2-a+1}-\dfrac{15}{\left(a+1\right)\left(a^2-a+1\right)}\)

\(=\dfrac{5a^2-5a+5+10a+10-15}{\left(a+1\right)\left(a^2-a+1\right)}\)

\(=\dfrac{5a^2+5a}{\left(a+1\right)\left(a^2-a+1\right)}=\dfrac{5a}{a^2-a+1}\)

TQ

Trần Quang Minh

1 tháng 12 2017

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

1

NN

Nguyễn Nam

1 tháng 12 2017

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

AV

Ánh Vũ Ngọc

12 tháng 11 2017

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, \(\dfrac{2}{x+y}\)...

1

PK

Phùng Khánh Linh

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

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

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

.....

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

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

TT

Trần Thị Bích Lam

15 tháng 11 2018

Quy đồng mẫu hai phân thức: a) \(\dfrac{5}{2x+6},\dfrac{3}{x^2-9}\) b)\(\dfrac{2x}{x^2-8x+16},\dfrac{x}{3x^2-12x}\) c)\(\dfrac{x+y}{x}\)và \(\dfrac{x}{x-y}\) d)\(\dfrac{2}{x^2+2xy}\)và \(\dfrac{1}{xy+2y^2}\) e)\(\dfrac{1}{x+2},\dfrac{8}{2x-x^2}\) d)\(x^2+1\),...

1

NL

Nguyễn Lê Phước Thịnh

20 tháng 11 2022

a: \(\dfrac{5}{2x+6}=\dfrac{5\left(x-3\right)}{2\left(x+3\right)\left(x-3\right)}\)

3/x^2-9=6/2(x+3)(x-3)

b: \(\dfrac{2x}{x^2-8x+16}=\dfrac{2x}{\left(x-4\right)^2}=\dfrac{6x^2}{3x\left(x-4\right)^2}\)

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

c: \(\dfrac{x+y}{x}=\dfrac{\left(x+y\right)\cdot\left(x-y\right)}{x\left(x-y\right)}\)

x/x-y=x^2/x(x-y)

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

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

NT

nguyễn thái hồng duyên

29 tháng 6 2018

Tính :

a)\(\dfrac{6x-3}{5x^2+x}.\dfrac{25x^2+10x+1}{1-8x^3}\)

b)\(\dfrac{3x^2-x}{x^2-1}.\dfrac{1-x^4}{\left(1-3x\right)^3}\)

c)\(\dfrac{x^4-xy^3}{2xy+y^2}:\dfrac{x^3+x^2y+xy^2}{2x+y}\)

d) \(\dfrac{5x^2-10xy+5y^2}{2x^2-2xy+2y^2}:\dfrac{8x-8y}{x^3+10y^3}\)

2

TT

Thành Trương

1 tháng 7 2018

Phân thức đại số

TT

Thành Trương

1 tháng 7 2018

Phân thức đại số

DN

Dân Nguyễn Chí

26 tháng 11 2017

Thực hiện phép tính: 1. \(\dfrac{x^2}{x+1}+\dfrac{2x}{x^2-1}-\dfrac{1}{1-x}+1\) 2. \(\dfrac{1}{x^3-x}-\dfrac{1}{\left(x-1\right)x}+\dfrac{2}{x^2-1}\) 3. \(\dfrac{y}{xy-5y^2}-\dfrac{15y-25x}{y^2-25x^2}\) 4. \(\dfrac{4-2x+x^2}{2+x}-2-x\) 5. \(\dfrac{2x^3-2y^3}{3x+3y}:\dfrac{2x^2+2xy+y^2}{x^2+2xy+y^2}\) 6....

1

NN

Nguyễn Nam

27 tháng 11 2017

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

NP

Nga Phạm

22 tháng 12 2017

thuc hien phep tinh a.\(\left(\dfrac{2x+1}{2x-1}-\dfrac{2x-1}{2x+1}\right):\dfrac{4x}{10x-5}\) b.\(\left(\dfrac{1}{x^2+1}-\dfrac{2-x}{x+1}\right):\left(\dfrac{1}{x}+1-2\right)\) c.\(\dfrac{1}{x-1}-\dfrac{x^3-x}{x^2+1}.\left(\dfrac{1}{x^2-2x+1}+\dfrac{1}{1-x^2}\right)\) d.\(\left(\dfrac{x^2+xy}{x^3+x^2y+xy^2+y^3}+\dfrac{y}{x^2+y^2}\right):\left(\dfrac{1}{x-y}-\dfrac{2xy}{x^3-x^2y+xy^2-y^3}\right)\) ...

1

NL

Nguyễn Lê Phước Thịnh

13 tháng 6 2022

a: \(=\dfrac{4x^2+4x+1-\left(4x^2-4x+1\right)}{\left(2x-1\right)\left(2x+1\right)}\cdot\dfrac{5\left(2x-1\right)}{4x}\)

\(=\dfrac{8x}{2x+1}\cdot\dfrac{5}{4x}=\dfrac{10}{2x+1}\)

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

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

TT

Triệu Tử Dương

11 tháng 12 2017

Thực hiện các phép tính sau: a).\(\left(\dfrac{2x+1}{2x-1}-\dfrac{2x-1}{2x+1}\right):\dfrac{4x}{10x-5}\) b). \(\left(\dfrac{1}{x^2+1}-\dfrac{2-x}{x+1}\right):\left(\dfrac{1}{x}+x-2\right)\) c). \(\dfrac{1}{x-1}-\dfrac{x^3-x}{x^2+1}.\left(\dfrac{1}{x^2-2x+1}+\dfrac{1}{1-x^2}\right)\) d)....

1

PT

Phương Trâm

11 tháng 12 2017

a) \(\left(\dfrac{2x+1}{2x-1}-\dfrac{2x-1}{2x+1}\right):\dfrac{4x}{10x-5}\)

\(=\left(\dfrac{\left(2x+1\right)\left(2x+1\right)}{2x^2-1}-\dfrac{\left(2x-1\right)\left(2x-1\right)}{2x^2-1}\right):\dfrac{4x}{10x-5}\)

\(=\left(\dfrac{\left(2x+1\right)^2-\left(2x-1\right)^2}{2x^2-1}\right):\dfrac{4x}{10x-5}\)

\(=\left(\dfrac{\left(2x+1-2x-1\right)\left(2x+1+2x-1\right)}{2x^2-1}\right):\dfrac{4x}{10x-5}\)

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

\(=\dfrac{5}{2x+1}\)

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

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

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

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

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

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

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

c) d) Tự làm đi mình làm biếng quass >.< ^^