Với \(x\ge-1\) thì \(\left|x+1\right|=x+1\)\(\Rightarrow A=\frac{x+1+2x}{3x^2-2x+1}=\frac{3x+1}{3x^2-2x+1}\)

         Thay \(x=\frac{3}{4}>-1\) vào ta được:\(A=\frac{3.\frac{3}{4}+1}{3.\left(\frac{3}{4}\right)^2-2.\frac{3}{4}+1}=\frac{52}{19}\)

Với \(x< -1\) thì \(\left|x+1\right|=-\left(x+1\right)=-x-1\)\(\Rightarrow A=\frac{-x-1+2x}{3x^2-2x+1}=\frac{x-1}{3x^2-2x+1}\)

      Thay \(x=-2< -1\) vào ta được \(A=\frac{-2-1}{3.\left(-2\right)^2-2.\left(-2\right)+1}=-\frac{3}{17}\)

ảnh lỗi r ạ

Lỗi rùi

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Lời giải:
1. 

$M=(x^2+6x+9)+(x^2-9)-2(x^2-2x-8)$

$=x^2+6x+9+x^2-9-2x^2+4x+16=(x^2+x^2-2x^2)+(6x+4x)+(9-9+16)$
$=10x+16=5(2x+1)+11=5.0+11=11$

2.

$V=(9x^2+24x+16)-(x^2-16)-10x=9x^2+24x+16-x^2+16-10x$

$=(9x^2-x^2)+(24x-10x)+(16+16)=8x^2+14x+32$

$=8(\frac{-1}{10})^2+14.\frac{-1}{10}+32=\frac{767}{25}$

3.

$P=(x^2+2x+1)-(4x^2-4x+1)+3(x^2-4)$

$=x^2+2x+1-4x^2+4x-1+3x^2-12$
$=(x^2-4x^2+3x^2)+(2x+4x)+(1-1-12)$

$=6x-12=6.1-12=-6$

4.

$Q=(x^2-9)+(x^2-4x+4)-2x^2+8x$

$=x^2-9+x^2-4x+4-2x^2+8x$
$=(x^2+x^2-2x^2)+(-4x+8x)-9+4$

$=4x-5=4(-1)-5=-9$

\(P=\dfrac{-x^4+2x^3-2x+1}{4x^2-1}+\dfrac{8x^2-4x+2}{8x^3+1}\)

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

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

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

bạn viết thế này khó nhìn quá

nhìn hơi đau mắt nhá bạn hoa mắt quá

\(M=4x^2-9-2x-10-2\left(x^2+x-2\right)\)

\(=4x^2-2x-19-2x^2-2x+4\)

\(=2x^2-4x-15\)

Khi x=0 thì M=-15

Bài 1 :

ĐKXĐ : \(x\ne3;x\ne-3\)

\(\frac{2}{x+3}+\frac{2}{x-3}+\frac{9x}{x^2-9}\)

\(=\frac{2\left(x-3\right)}{\left(x+3\right)\left(x-3\right)}+\frac{2\left(x+3\right)}{\left(x-3\right)\left(x+3\right)}+\frac{9x}{\left(x-3\right)\left(x+3\right)}\)

\(=\frac{2\left(x-3\right)+2\left(x+3\right)+9x}{\left(x+3\right)\left(x-3\right)}\)

\(=\frac{2x-6+2x+6+9x}{\left(x+3\right)\left(x-3\right)}\)

\(=\frac{13x}{x^2-9}\)

Bài 2 :

a) \(\left(2x-3\right)^2-1=3\)

\(\Leftrightarrow\left(2x-3\right)^2-4=0\)

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

\(\Leftrightarrow\left(2x-5\right)\left(2x-1\right)=0\)

\(\Rightarrow\orbr{\begin{cases}2x-5=0\\2x-1=0\end{cases}\Rightarrow\orbr{\begin{cases}x=\frac{5}{2}\\x=\frac{1}{2}\end{cases}}}\)

b) \(2x^2-5x-12=0\)

\(2x^2-8x+3x-12=0\)

\(2x\left(x-4\right)+3\left(x-4\right)=0\)

\(\left(x-4\right)\left(2x+3\right)=0\)

\(\Rightarrow\orbr{\begin{cases}x-4=0\\2x+3=0\end{cases}\Rightarrow\orbr{\begin{cases}x=4\\x=\frac{-3}{2}\end{cases}}}\)

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