ĐKXĐ : \(\left\{{}\begin{matrix}4x^2-1\ne0\\8x^3+1\ne0\end{matrix}\right.\Leftrightarrow x\ne\pm\dfrac{1}{2}\)

\(P=\dfrac{2x^5-x^4-2x+1}{4x^2-1}+\dfrac{8x^2-4x+2}{8x^3+1}\)

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

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

https://sg.docworkspace.com/l/sIM-LioBEocfloAY

a, `(8x^3-4x^2): 4x -(4x^2-5x) : 2x + (2x)^2`

`=4x (2x^2-x) : 4x - 2x(2x-5/2 ) :2x + 4x^2`

`=2x^2-x-2x+5/2+4x^2`

`=6x^2-3x+5/2`

b, `(3x^3-x^2y) :x^2 -(xy^2+x^2y) :xy + 2x(x+1)`

`=x^2 (3x-y) :x^2 -xy(y+x) + (2x^2+2x)`

`=3x-y-y-x+2x^2+2x`

`=2x^2+4x-2y`

\(A=\left\{2x-3\left(x-1\right)-5\left[x-4\left(3-2x\right)+10\right]\right\}.\left(-2x\right)\)

\(=\left\{2x-3x+3-5\left[x-12+8x+10\right]\right\}.\left(-2x\right)\)

\(=\left\{-x+3-5\left(7x-2\right)\right\}.\left(-2x\right)\)

\(=\left(-x+3-35x+10\right).\left(-2x\right)\)

\(=\left(-36x+13\right).\left(-2x\right)\)

\(=72x^2-26x\)

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

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

TH1: x>=1

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

TH2: 1/2<=x<1

\(A=\dfrac{1}{\sqrt{2}}\left(1-\sqrt{2x-1}-\sqrt{2x-1}-1\right)=-\sqrt{4x-2}\)

2: 

\(=\sqrt{x-1+6\sqrt{x-1}+9}-\sqrt{x-2-2\sqrt{x-2}+1+3}\)

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

=[x(x-2)/2(x²+4)-2x²/(4+x²)(2-x)][x(x-2)(x+1)/x³]

={[x(x-2)(2-x)-4x² ]/2(2-x)(4+x²)} .[x(x-2)(x+1)/x³ ]

=[-x(x²+4)/2(2-x)(4+x²)].[x(x-2)(x+1)/x³ ]

=-x.x(x-2)(x+1)/2(2-x)x³

=(x+1)/2x

uầy ,bn cứ nhân vào là đc

Thôi giúp luôn  =.=

\(\left(x+3\right)^2+\left(2x+1\right)\left(3x-5\right)-2x\left(3-x\right)+4x+25\)

\(=x^2+6x+9+6x^2-10x+3x-5-6x+2x^2+4x+25\)

\(=9x^2-3x+29\)

\(\left(x+3\right)^2+\left(2x+1\right)\left(3x-5\right)-2x\left(3-x\right)+4x+25\)

\(=x^2+6x+9+6x^2-10x+3x-5-6x+2x^2+4x+25\)

\(=9x^2-3x+29\)

hok tốt!

\(\left(2x-1\right)\left(2x+1\right)+4x\left(1-x\right)\)

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

\(=4x^2-1+4x-4x^2\)

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

\(=\left(4x-1\right)+0\)

\(=4x-1\)

(2x-1)(2x+1)+4x(1-x)

=\(4x^2-1\)+ 4x -\(4x^2\)

=4x-1

\(\left(2x-1\right)\left(2x+1\right)+4x\left(1-x\right)\)

\(=4x^2+2x-2x-1+4x-4x^2\)

\(=4x-1\)