Question

factorize
$\frac{a}{x - b} + \frac{b}{x - a} = 2$
​

Answer 1

Take LCM and cross multiply, then we get the equation

$2 {x}^{2} - 3ax - 3bx + {a}^{2} + {b}^{2} + 2ab = 0$

$= > \: 2 {x}^{2} - 3x(a + b) + {(a + b)}^{2} = 0$

$= > \: 2 {x}^{2} - 2x(a + b) - x(a + b) + {(a + b)}^{2} = 0$

$2x(x - a - b) - (a + b)(x - a - b) = 0$

$= > (x - a - b)(2x - a - b)$

are the required factors

• I hope it will help you. Thank you