Question

The Expression [x³/x-1 - x²/X+1 - 1/x-1+ 1/X+1] is :​

Answer 1

Answer:

$\bf\red{( \frac{ {x}^{3} }{x - 1} - \frac{1}{x - 1} ) - ( \frac{ {x}^{2} }{x + 1} - \frac{1}{ x + 1} )}$

$\bf\red{ = \frac{ {x}^{3} - 1 }{x - 1} - \frac{ {x}^{2} - 1 }{x + 1} }$

$\bf\red{ = \frac{(x - 1)( {x}^{2} + x + 1) }{x - 1} - \frac{(x - 1)(x + 1)}{x + 1} }$

$\bf\red{ = ( {x}^{2} + x + 1) - (x - 1)}$

$\bf\red{ = {x}^{2} + 2}$

Hope it will be helpful :) ....✍️

Answer 2

Answer:-

${( \frac{ {x}^{3} }{x - 1} - \frac{1}{x - 1} ) - ( \frac{ {x}^{2} }{x + 1} - \frac{1}{ x + 1} )}$

${ = \frac{ {x}^{3} - 1 }{x - 1} - \frac{ {x}^{2} - 1 }{x + 1} }$

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

${ = ( {x}^{2} + x + 1) - (x - 1)}$

${ = {x}^{2} + 2}$