\(=\dfrac{-3\left(x-1\right)}{\left(1+x\right)^2}\cdot\dfrac{x+1}{6\left(x-1\right)\left(x+1\right)}\left(x\ne\pm1\right)\\ =\dfrac{-1}{2\left(x+1\right)^2}\)

\(a,=\dfrac{x+3\sqrt{x}+2+2x-4\sqrt{x}-2-5\sqrt{x}}{\left(\sqrt{x}-2\right)\left(\sqrt{x}+2\right)}\\ =\dfrac{3x-6\sqrt{x}}{\left(\sqrt{x}-2\right)\left(\sqrt{x}+2\right)}=\dfrac{3\sqrt{x}\left(\sqrt{x}-2\right)}{\left(\sqrt{x}-2\right)\left(\sqrt{x}+2\right)}=\dfrac{3\sqrt{x}}{\sqrt{x}+2}\\ b,=2a-6b+6b-5a=-3a\)

\(a,=1-2x+x^2+2x-x^2=1\\ b,=\dfrac{\left(x+2\right)^2}{x+2}=x+2\)

1: \(4xy\left(x^2-2xy+3y^2\right)=4x^3y-8x^2y^2+12xy^3\)

2: \(\left(x^2-2\right)\left(x^4+2x^2+4\right)=x^6-8\)

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

(x²-1)(x²+x+1)(x²-x+1)

=(x²-1)[(x²+1)²-x²]

=(x²-1)[x⁴+2x²+1-x²]

=(x²-1)(x⁴+x²+1)

=(x²)³-1

=x⁶-1

( x² - 1 )( x² + x + 1 )( x² - x + 1 )

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

= ( x² - 1 )[ ( x² + 1 )² - x² ]

= ( x² - 1 )( x⁴ + 2x² + 1 - x² )

= ( x² - 1 )( x⁴ + x² + 1 )

= x⁶ + x⁴ + x² - x⁴ - x² - 1

= x⁶ - 1 

\(\left(x^2-1\right)\left(x^2+x+1\right)\left(x^2-x+1\right)=\left(x^2-1\right)\left(x^4+x^2+1\right)=x^6-1\)

\(=\dfrac{1}{x}-\dfrac{1}{x+1}+\dfrac{1}{x+1}-\dfrac{1}{x+2}+...+\dfrac{1}{x+2013}-\dfrac{1}{x+2014}\)

=1/x-1/x+2014

\(=\dfrac{x+2014-x}{x\left(x+2014\right)}=\dfrac{2014}{x\left(x+2014\right)}\)

a) biết chết liền

b) \(\left(x^2-xy+y^2\right)\left(x+y\right)=x^3+y^3\)

(8 - 5x).(x + 2) + 4.(x - 2)(x - 1) + 2.(x - 2)(x + 2) + 10

= (8x + 16 - 5x² - 10x) + 4.(x² - 3x + 2) + 2.(x² - 4) + 10

= 8x + 16 - 5x² - 10x + 4x² - 12x + 8 + 2x² - 8 + 10

= (8x - 10x - 12x) + (-5x² + 4x² + 2x²) + (16 + 8 - 8 + 10)

= -14x + x² + 26