Với `x \ne +-2,x \ne 1/2,x \ne0`. Ta có:

`(3/[2x+4]+x/[2-x]+[2x^2+3]/[x^2-4]):[2x-1]/[4x-8]`

`=(3/[2(x+2)]-x/[x-2]+[2x^2+3]/[(x-2)(x+2)]).[4(x-2)]/[2x-1]`

`=[3(x-2)-2x(x+2)+2(2x^2+3)]/[x(x-2)(x+2)].[4(x-2)]/[2x-1]`

`=[3x-6-2x^2-4x+4x^2+6]/[x(x+2)]. 4/[2x-1]`

`=[2x^2-x]/[x(x+2)]. 4/[2x-1]`

`=[x(2x-1)]/[x(x+2)] . 4/[2x-1]`

`=4/[x+2]`

a: \(P=\left(\dfrac{3}{2\left(x+2\right)}-\dfrac{x}{x-2}+\dfrac{2x^2+3}{\left(x-2\right)\left(x+2\right)}\right)\cdot\dfrac{4\left(x-2\right)}{2x-1}\)

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

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

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

b: Khi 4x²-1=0 thì (2x-1)(2x+1)=0

=>x=1/2(loại) và x=-1/2(nhận)

Khi x=-1/2 thì \(P=\left(2\cdot\dfrac{-1}{2}\right):\left(-\dfrac{1}{2}+2\right)=-1:\dfrac{3}{2}=-\dfrac{2}{3}\)

Bài 1 : 

\(\left(x-2\right)^2-\left(x-3^2\right)=\left(x-2\right)^2-\left(x-9\right)\)

\(=x^2-4x+4-x+9=x^2-5x+13\)

Bài 2 : 

a, \(P=\frac{1-4x^2}{4x^2-4x+1}=\frac{\left(1-2x\right)\left(2x+1\right)}{\left(2x-1\right)^2}\)

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

b, Thay x = -4 ta được : 

\(\frac{-2.\left(-4\right)-1}{2.\left(-4\right)-1}=\frac{8-1}{-8-1}=-\frac{7}{9}\)

1:

a: \(\left(2x-5\right)^2-4x\left(x+3\right)\)

\(=4x^2-20x+25-4x^2-12x\)

=-32x+25

b: \(\left(x-2\right)^3-6\left(x+4\right)\left(x-4\right)-\left(x-2\right)\left(x^2+2x+4\right)\)

\(=x^3-6x^2+12x-8-\left(x^3-8\right)-6\left(x^2-16\right)\)

\(=-6x^2+12x-6x^2+96=-12x^2+12x+96\)

c: \(\left(x-1\right)^2-2\left(x-1\right)\left(x+2\right)+\left(x+2\right)^2+5\left(2x-3\right)\)

\(=\left(x-1-x-2\right)^2+5\left(2x-3\right)\)

\(=\left(-3\right)^2+5\left(2x-3\right)\)

\(=9+10x-15=10x-6\)

2: 

a: \(\left(2-3x\right)^2-5x\left(x-4\right)+4\left(x-1\right)\)

\(=9x^2-12x+4-5x^2+20x+4x-4\)

\(=4x^2+12x\)

b: \(\left(3-x\right)\left(x^2+3x+9\right)+\left(x-3\right)^3\)

\(=27-x^3+x^3-9x^2+27x-27\)

\(=-9x^2+27x\)

c: \(\left(x-4\right)^2\left(x+4\right)-\left(x-4\right)\left(x+4\right)^2+3\left(x^2-16\right)\)

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

\(=\left(x^2-16\right)\left(-8\right)+3\left(x^2-16\right)\)

\(=-5\left(x^2-16\right)=-5x^2+80\)

\(1,=-x^2+2x+15+2x^2+5x-3=x^2+7x+12\\ 2,=-4x\left(x^2-x-12\right)-3x^3+3x^2-3x\\ =-4x^3+4x^2+48x-3x^3+3x^2-3x\\ =-7x^3+7x^2+45x\)

1) (-x+5)(x+3)+(2x-1)(x+3)

=(x+3)(-x+5+2x-1)=(x+3)(x-4)\(=X^2-4x+3x-12=x^2-x-12\)

\(2) -4x(x+3)(x-4)-3x(x^2-x+1)=(-4x^2-12x)(x-4)-3x^3+3x^2-3x=-4x^3-12x^2-12x^2+48x-3x^3+3x^2-3x=-7x^3-12x^2-45x\)

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

Để biểu thức trên nhận giá trị âm khi \(\dfrac{\left(x-2\right)^2}{x^3-2x^2-4x+8}< 0\)

\(\Rightarrow x^3-2x^2-4x+8< 0\)do \(\left(x-2\right)^2\ge0\)

\(\Leftrightarrow\left(x+2\right)\left(x^2-2x+4\right)-2x\left(x+2\right)< 0\)

\(\Leftrightarrow\left(x+2\right)\left(x-2\right)^2< 0\Leftrightarrow x< -2\)

Em ơi mình đăng bài sang bên môn toán nha