Question

please tell me my answer​

Answer 1

$\mathsf{Consider :\;\dfrac{x^2 + x + 2}{x^2 - x^3}}$

Taking x common in both Numerator and Denominator, We get :

$\mathsf{\implies \dfrac{x\bigg[x + 1 + \dfrac{2}{x}\bigg]}{x(x - x^2)}}$

$\mathsf{\implies \dfrac{\bigg[\bigg(x + \dfrac{2}{x}\bigg) + 1\bigg]}{x - x^2}}$

$\mathsf{Given :\;x + \dfrac{2}{x} = 1}$

$\mathsf{\implies \dfrac{1 + 1}{x - x^2}}$

$\mathsf{\implies \dfrac{2}{x - x^2}}$

$\mathsf{Now,\;Consider :\;x + \dfrac{2}{x} = 1}$

$\mathsf{\implies \dfrac{x^2 + 2}{x} = 1}$

$\mathsf{\implies x^2 + 2 = x}$

$\mathsf{\implies x - x^2 = 2}$

$\mathsf{Substituting\;the\;value\;of\;(x - x^2)\;in\;\dfrac{2}{x - x^2},\;We\;get :}$

$\mathsf{\implies \dfrac{2}{2} = 1}$

$\underline{\mathbf{Answer}} : \mathsf{Value\;\;of\;\;\dfrac{x^2 + x + 2}{x^2 - x^3}\;\;is\;\;\boxed{\mathbf{1}}}$