Question

question show that and solve this​

Answer 1

Step-by-step explanation:

$\frac{ {a}^{ - 1} }{ {a}^{ - 1} + {b}^{ - 1}} + \frac{ {a}^{ - 1} }{ {a}^{ - 1} - {b}^{ - 1}} = \frac{2 {b}^{2} }{ {b}^{2} - {a}^{2} } \\ LHS = \frac{ {a}^{ - 1} }{ {a}^{ - 1} + {b}^{ - 1}} + \frac{ {a}^{ - 1} }{ {a}^{ - 1} - {b}^{ - 1}} \\ = \frac{ \frac{1}{a} }{ \frac{1}{a} + \frac{1}{b} } + \frac{ \frac{1}{a} }{ \frac{1}{a} - \frac{1}{b} } \\ = \frac{ \frac{1}{a} }{ \frac{b + a}{ab} } + \frac{ \frac{1}{a} }{ \frac{b - a}{ab} } \\ = \frac{ab}{a(b + a)} + \frac{ab}{a(b - a)} \\ = \frac{b}{(b + a)} + \frac{b}{(b - a)} \\ = \frac{b \{b - a + b + a \}}{(b + a)(b - a)} \\ = \frac{b \{2b \}}{(b^{2} - a^{2}) } \\ = \frac{2b^{2}}{b^{2} - a^{2}} \\ = RHS$

Thus proved