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

\(=2x\left(4x^2-4x+1\right)-3x\left(x^2-9\right)-4x\left(x^2+2x+1\right)\)

\(=8x^3-8x^2+2x-3x^3+27x-4x^3-8x^2-4x\)

\(=x^3-16x^2+25x\)

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

\(=3x+6\sqrt{x}-\left(x-1\right)\)

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

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

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

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

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

\(=-x+8\sqrt{x}+1\)

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

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

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

\(=4x-3\sqrt{x}-3\)

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

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

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

\(=-x+3\sqrt{x}-7\)

\(E=\left(\sqrt{x}+4\right)\left(\sqrt{x}-4\right)-2\left(2\sqrt{x}-1\right)\left(\sqrt{x}+2\right)\)

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

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

\(=x-4-4x-6\sqrt{x}+4\)

\(=-3-6\sqrt{x}\)

\(=x^3-27-4x^2+4x-1=x^3-4x^2+4x-28\)

thank you!

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

\(=25-9x^2-x^3-3x^2-3x-1\)

\(=-x^3-12x^2-3x+24\)

cảm ơn nha!

\(C=\left\lbrack\frac{1}{1+x}+\frac{2x}{1-x^2}\right\rbrack:\left(\frac{1}{x}-1\right)\)

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

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

\(D=\frac{x^2-y^2}{x+y}\cdot\frac{\left(x+y\right)^2}{x}+\frac{y^2}{x+y}\cdot\frac{\left(x+y\right)^2}{x}\)

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

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

\(=\frac{\left|x-3\right|}{\left.\left(x-3\right)\left(x+3\right)\right.}\cdot\left(x-3\right)^2=\frac{\left|x-3\right|\cdot\left(x-3\right)}{x+3}\)

\(F=\frac{\sqrt{x}}{\sqrt{x}-5}-\frac{10\sqrt{x}}{x-25}-\frac{5}{\sqrt{x}+5}\)

\(=\frac{\sqrt{x}\left(\sqrt{x}+5\right)-10\sqrt{x}-5\left(\sqrt{x}-5\right)}{\left(\sqrt{x}-5\right)\left(\sqrt{x}+5\right)}\)

\(=\frac{x-5\sqrt{x}-5\sqrt{x}+25}{\left(\sqrt{x}-5\right)\left(\sqrt{x}+5\right)}=\frac{\left(\sqrt{x}-5\right)^2}{\left(\sqrt{x}-5\right)\left(\sqrt{x}+5\right)}\)

\(=\frac{\sqrt{x}-5}{\sqrt{x}+5}\)

a: ĐKXĐ: x<>1; x<>-1

TH1: \(x^2-1>0\)

=>\(x^2>1\)

=>x>1 hoặc x<-1

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

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

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

TH2: \(x^2-1<0\)

=>-1<x<1

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

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

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

b: \(B=2x:\frac12x+\left(x+1\right)^2\)

\(=\left(2:\frac12\right)\cdot\left(\frac{x}{x}\right)+x^2+2x+1\)

\(=x^2+2x+1+4=x^2+2x+5\)

c: \(C=\left\lbrack\frac{1}{1+x}+\frac{2x}{1-x^2}\right\rbrack:\left(\frac{1}{x}-1\right)\)

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

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

d: \(D=\frac{x^2-y^2}{x+y}\cdot\frac{\left(x+y\right)^2}{x}+\frac{y^2}{x+y}\cdot\frac{\left(x+y\right)^2}{x}\)

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

e: \(E=\frac{\left|x-3\right|}{x^2-9}\left(x^2-6x+9\right)\)

\(=\frac{\left|x-3\right|}{\left.\left(x-3\right)\left(x+3\right)\right.}\cdot\left(x-3\right)^2=\frac{\left|x-3\right|\cdot\left(x-3\right)}{x+3}\)

f: \(F=\frac{\sqrt{x}}{\sqrt{x}-5}-\frac{10\sqrt{x}}{x-25}-\frac{5}{\sqrt{x}+5}\)

\(=\frac{\sqrt{x}\left(\sqrt{x}+5\right)-10\sqrt{x}-5\left(\sqrt{x}-5\right)}{\left(\sqrt{x}-5\right)\left(\sqrt{x}+5\right)}\)

\(=\frac{x-5\sqrt{x}-5\sqrt{x}+25}{\left(\sqrt{x}-5\right)\left(\sqrt{x}+5\right)}=\frac{\left(\sqrt{x}-5\right)^2}{\left(\sqrt{x}-5\right)\left(\sqrt{x}+5\right)}\)

\(=\frac{\sqrt{x}-5}{\sqrt{x}+5}\)

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

(x² + 1)(x - 3) - (x - 3)(x² - 1)
= [x² + 1 - (x² - 1)](x - 3)

= (x² + 1 - x² + 1)(x - 3)

= 2(x - 3)

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

=x^2-2x+2x-4-x^2-x-3x-3

=-4x-7