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prove that a -1 /a -1 +b -1 + a -1 / a -1 - b -1 = – ( 2b ) 2 / a 2 – b 2

prove  that a-1/a-1 +b-1     +   a -1 / a-1 - b-1 =  – ( 2b ) / a2 – b2

Grade:9

1 Answers

Sumit Majumdar IIT Delhi
askIITians Faculty 137 Points
7 years ago
Dear student,
We have:
\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{b}{b+a}+\frac{b}{b-a}=b\left[\frac{b-a+b+a}{b^{2}-a^{2}}\right]=\frac{2b^2}{b^2-a^2}Regards
Sumit

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