Bạn gõ cái này nhé 

a: \(A=\dfrac{x+5}{2x}+\dfrac{x-6}{x-5}-\dfrac{2x^2-2x-50}{2x\left(x-5\right)}\)

\(=\dfrac{x^2-25+2x^2-12x-2x^2+2x+50}{2x\left(x-5\right)}\)

\(=\dfrac{x^2-10x+25}{2x\left(x-5\right)}=\dfrac{x-5}{2x}\)

b: Để A=1/3 thì x-5/2x=1/3

=>3x-15=2x

=>x=15

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

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

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

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

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

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

Có vài bước mình làm tắc á nha :>

Bài 1:

\(P=2a^2-2b^2-a^2+2ab-b^2+a^2+2ab+b^2+b^2=2a^2-b^2+4ab\\ Q=\left(2x+3\right)^2+\left(2x-3\right)^2-2\left(2x-3\right)\left(2x+3\right)\\ Q=\left(2x+3-2x+3\right)^2=9^2=81\)

Bài 2:

\(Sửa:A=x^2+2xy+y^2-4x-4y+2=\left(x+y\right)^2-4\left(x+y\right)+4-2\\ A=\left(x+y-2\right)^2-2=\left(3-2\right)^2-2=1-2=-1\)

a: \(A=\left[\left(\dfrac{4x}{x+2}+\dfrac{8x^2}{4-x^2}\right)\right]:\left[\dfrac{x-1}{x^2-2x}-\dfrac{2}{x}\right]\)

\(=\left(\dfrac{4x}{x+2}-\dfrac{8x^2}{\left(x-2\right)\left(x+2\right)}\right):\left(\dfrac{x-1}{x\left(x-2\right)}-\dfrac{2}{x}\right)\)

\(=\dfrac{4x\left(x-2\right)-8x^2}{\left(x+2\right)\left(x-2\right)}:\dfrac{x-1-2\left(x-2\right)}{x\left(x-2\right)}\)

\(=\dfrac{-8x}{\left(x-2\right)\left(x+2\right)}\cdot\dfrac{x\left(x-2\right)}{x-1-2x+4}\)

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

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

b: \(x^2+2x=15\)

=>\(x^2+2x-15=0\)

=>(x+5)(x-3)=0

=>\(\left[{}\begin{matrix}x+5=0\\x-3=0\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=-5\left(nhận\right)\\x=3\left(loại\right)\end{matrix}\right.\)

Thay x=-5 vào A, ta được:

\(A=\dfrac{8\cdot\left(-5\right)^2}{\left(-5-3\right)\left(-5+2\right)}=\dfrac{8\cdot25}{\left(-8\right)\cdot\left(-3\right)}=\dfrac{25}{3}\)

c: |A|>A

=>A<0

=>\(\dfrac{8x^2}{\left(x-3\right)\left(x+2\right)}< 0\)

=>(x-3)(x+2)<0

TH1: \(\left\{{}\begin{matrix}x-3>0\\x+2< 0\end{matrix}\right.\)

=>\(\left\{{}\begin{matrix}x>3\\x< -2\end{matrix}\right.\)

=>\(x\in\varnothing\)

TH2: \(\left\{{}\begin{matrix}x-3< 0\\x+2>0\end{matrix}\right.\)

=>\(\left\{{}\begin{matrix}x< 3\\x>-2\end{matrix}\right.\)

=>-2<x<3

Kết hợp ĐKXĐ, ta được: \(\left\{{}\begin{matrix}-2< x< 3\\x\notin\left\{0;2\right\}\end{matrix}\right.\)

a: |2x-3|=1

=>2x-3=1 hoặc 2x-3=-1

=>x=1(nhận) hoặc x=2(loại)

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

b: ĐKXĐ: x<>-1; x<>2

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

a)    \(A=\frac{x\left(x+1\right)}{\left(x-1\right)^2}:\left(\frac{x^2-1+x+2-x^2}{x\left(x-1\right)}\right)\)

<=> \(A=\frac{x\left(x+1\right)}{\left(x-1\right)^2}.\frac{x\left(x-1\right)}{x+1}\)

<=> \(A=\frac{x^2}{x-1}\)

b) \(|2x+1|=3\)

TH1: 2x+1=3 \(\left(x\ge\frac{-1}{2}\right)\)

    => x=1 (TM)

TH2: 2x+1=-3 \(\left(x< \frac{-1}{2}\right)\)

    => x=-2 (TM)

c)     \(A< 3\)

<=> \(\frac{x^2}{x-1}< 3\)

<=> \(\frac{x^2-3x+3}{x-1}< 0\)

 =>  \(x< 1\)

\(A=\frac{x^2+x}{x^2-2x+1}:\left(\frac{x+1}{x}-\frac{1}{1-x}+\frac{2-x^2}{x^2-x}\right)\left(x\ne0;x\ne1\right)\)

\(\Leftrightarrow A=\frac{x\left(x+1\right)}{\left(x-1\right)^2}:\left(\frac{x+1}{x}+\frac{1}{x-1}+\frac{2-x^2}{x\left(x-1\right)}\right)\)

\(\Leftrightarrow A=\frac{x\left(x+1\right)}{\left(x-1\right)^2}:\left(\frac{\left(x-1\right)\left(x+1\right)}{x\left(x-1\right)}+\frac{x}{x\left(x-1\right)}+\frac{2-x^2}{x\left(x-1\right)}\right)\)

\(\Leftrightarrow A=\frac{x\left(x+1\right)}{\left(x-1\right)^2}:\left(\frac{x^2-1}{x\left(x-1\right)}+\frac{x}{x\left(x-1\right)}+\frac{2-x^2}{x\left(x-1\right)}\right)\)

\(\Leftrightarrow A=\frac{x\left(x+1\right)}{\left(x-1\right)^2}:\frac{x^2-1+x+2-x^2}{x\left(x-1\right)}\)

\(\Leftrightarrow A=\frac{x\left(x+1\right)}{\left(x-1\right)^2}:\frac{x+1}{x\left(x-1\right)}\)

\(\Leftrightarrow A=\frac{x\left(x+1\right)}{\left(x-1\right)^2}\cdot\frac{x\left(x-1\right)}{x+1}=\frac{x^2}{x-1}\)

\(A=\frac{x^2}{x-1}\left(x\ne0;x\ne1\right)\)

\(|2x+1|=3\)

\(\Leftrightarrow\orbr{\begin{cases}2x+1=3\\2x+1=-3\end{cases}\Leftrightarrow\orbr{\begin{cases}2x=2\\2x=-4\end{cases}\Leftrightarrow}\orbr{\begin{cases}x=1\left(loại\right)\\x=-2\left(tm\right)\end{cases}}}\)

Thay x=-2 vào A, ta có: \(A=\frac{2^2}{2-1}=\frac{4}{1}=4\)

Vậy \(A=4\)khi \(|2x+1|=3\)