Question

pls give the solution for this one​

Answer 1

Answer:

Step-by-step explanation:

To prove: $\frac{a^{-1}}{a^{-1}+b^{-1}}$  + $\frac{a^{-1}}{a^{-1}-b^{-1}}$  = $\frac{2b^2}{b^2-a^2}$

take LHS

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

= $\frac{a^{-1}*(a^{-1}-b^{-1}) + a^{-1}*(a^{-1}+b^{-1})} {(a^{-1}+b^{-1}) * (a^{-1}-b^{-1})}$

= $\frac{ a^{-2}- a^{-1}*b^{-1} + a^{-2} + a^{-1}*b^{-1} }{a^{-2} - b^{-2}}$

= $\frac{2*a^{-2}}{a^{-2}-b^{-2}}$

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

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

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

= $\frac{2b^2}{b^2-a^2}$  = RHS

=> LHS = RHS

Hence proved