Question

resolve into partial fraction ​

Answer 1

${\bold {\huge{\mathcal {ANSWER-}}}}$

$\int \: \frac{(x - 2)}{x( - x - 1)}$

by partial fraction

$\frac{(x - 2)}{x( - x - 1)} = \frac{A}{x} + \frac{B}{( - x - 1)}$

$(x - 2) = A( - x - 1) + Bx$

now let

$x = - 1$

$(1 - 2) = A( 1 - 1) + B \times 1$

${\bold {\large {\boxed {B=-1}}}}$

on comparing and subtituting the value in B :

$- 2 = - A + ( - 1)$

${\bold {\large {\boxed {</p><p>A=1}}}}$

so the answer will be

$log|x| \: - log| - x - 1| + c$