Bài 5: Phép cộng các phân thức đại số

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

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

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

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

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

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

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

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

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

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

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

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

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

[2a^2-11ab]/[2ab]+[5b-a]/b+[a+2b]/a`      `ĐK: a,b \ne 0`

`=[2a^2-11ab+2a(5b-a)+2b(a+2b)]/[2ab]`

`=[2a^2-11ab+10ab-2a^2+2ab+4b^2]/[2ab]`

`=[ab+4b^2]/[2ab]`

`=[b(a+4b)]/[2ab]=[a+4b]/[2a]`

a, ĐKXĐ:\(\left\{{}\begin{matrix}x^2-1\ne0\\x+1\ne0\\x-1\ne0\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}x\ne\pm1\\x\ne-1\\x\ne1\end{matrix}\right.\Leftrightarrow x\ne\pm1\)

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

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

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

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

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

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

\(\Rightarrow P=\dfrac{2x}{x+1}\)

c, Thay x=2 vào P ta có:

\(P=\dfrac{2x}{x+1}=\dfrac{2.2}{2+1}=\dfrac{4}{3}\)

Đăng nhỏ lại dc ko 

Bài 1: 

a: =8xy/2x=4y

b: \(=\dfrac{4x-1-7x+1}{3x^2y}=\dfrac{-3x}{3x^2y}=\dfrac{-1}{xy}\)

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

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

câu 3 bài 1: = (x-y)(y-1)

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

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

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