\(=x^3+1\)

\(=x^3+1\)

(x – 1)(x + 1)(x + 2)

= ( x 2  + x – x – 1)(x + 2)

= ( x 2 – 1)(x + 2)

=  x 2 ( x + 2) – 1.(x +2)

=  x 3  + 2 x 2  – x – 2

`@` `\text {Ans}`

`\downarrow`

`x(1-x) + (x-1)^2`

`= x-x^2 + x^2 - 2x + 1`

`= (x-2x) + (-x^2 + x^2) + 1`

`= -x+1`

x ( 1 - x ) + ( x - 1 )² = x - x² + x² - 2x + 1 = -x + 1 = 1 - x

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

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

\(=\dfrac{1}{x+1}\)

(1-x)^2-x(x-1)

\(=x^2-4x+4+3x-x^2+3-x=-2x+7\)

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

\(\left(x+2\right)^2-\left(x-3\right)\left(x+1\right)=x^2+4x+4-\left(x^2+x-3x-3\right)=x^2+4x+4-x^2-x+3x+3=6x+7.\)

\(=\left(x^2+x-2\right)\left(x-3\right)\\ =x^3-3x^2+x^2-3x-2x+6\\ =x^3-2x^2-5x+6\)