Question

one by x minus a minus b is equals to 1 by x minus 1 by a minus 1 by b

Answer 1

$\frac{1}{x \: - \: a \: - \: b} \: = \: \frac{1}{x} \: - \: \frac{1}{a} \: - \: \frac{1}{b}$
$\frac{1}{x \: - \: a \: - \: b} \: - \: \frac{1}{x} \: = \: - \frac{1}{a} \: - \: \frac{1}{b}$
$\frac{x \: - \: (x \: - \: a \: - \: b)}{x(x \: - \: a \: - \: b) } \: = \: - ( \frac{a \: + \: b}{ab} )$
$\frac{(a \: + \: b)}{( {x}^{2} \: - \: (a \: + \: b)x ) } \: = \: - 1 \: \times \: \frac{( a \: + \: b)}{ab}$
$ab \: = \: ( - {x}^{2} \: + \: (a \: + \: b)x)$
${x}^{2} \: - \: (a \: + \: b)x \: + \: ab \: = \: 0$
${x}^{2} \: - \: ax \: - \: bx \: + \: ab \: = \: 0$
$x(x \: - \: a) \: - \: b(x \: - \: a) \: = \: 0$
$(x \: - \: a)(x \: - \: b) \: = \: 0$
$x \: = \: a \: \: and \: \: b$
Therefore,
x = a, b