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

jeeva , 11 Years ago

Grade 9

1 Answers

Sumit Majumdar

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

Approved

Last Activity: 11 Years ago

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