Question

1 by x minus 1 by X + b equal to 1 by a minus 1 by a + b ( x not is equal to 0,_b​

Answer 1

Answer:

$\frac{ \frac{1}{x - 1} }{x} + b \: \: = \frac{1}{a} - \frac{1}{a + b} \\ \\ (\frac{1}{x - 1} \times \frac{1}{x}) + b \: \: = \frac{a + b - a}{ {a}^{2} + ab} \\ \\ \frac{1}{ {x}^{2} - x } + b \: \: = \frac{b}{ {a}^{2} + ab } \\ \\ \frac{1 + b {x}^{2} - bx }{ {x}^{2} - x } \: \: = \: \: \frac{b}{ {a}^{2} + ab } \\ \\ by \: cross \: multiplying \\ \\ {a}^{2} + {a}^{2} b {x}^{2} - {a}^{2} bx + ab + a {b}^{2} {x}^{2} - a {b}^{2} x \: \: = \: \: b {x}^{2} - bx$