Question

$\frac{\frac{b}{a}- \frac{a}{b} }{\frac{1}{a}- \frac{1}{b} } =a+b$explain

Answer 1

Answer:

Given

$\frac{b}{a} - \frac{a}{b} \: \: = \: \: \frac{ {b}^{2} - {a}^{2} }{ab} - - (1) \\ \frac{1}{a} - \frac{1}{b} = \frac{b - a}{ab} - - - - (2)$

Now joining both (1) & (2)

$\frac{ \frac{ {b}^{2} - {a}^{2} }{ab} }{ \frac{b - a}{ab} } = \frac{ {b}^{2} - {a}^{2} }{ab} \times \frac{ab}{b - a} = \frac{(b + a)(b - a)}{ab} \times \frac{ab}{b - a} \\ cancelling \: ab \: \: and \: (b - a) \: \: = b + a$