Question

In the above question we have to proof...... Plz answer me fast

Answer 1

$Given : \frac{(a + \frac{1}{b})^m * (a - \frac{1}{b})^n }{(b + \frac{1}{a})^m * (b - \frac{1}{a} )^n}$

$= \ \textgreater \ \frac{ \frac{(ab + 1)^m}{b^m} * \frac{(ab - 1)^n}{b^n} }{ \frac{(ab + 1)}{a^m} * \frac{(ab-1)^n}{a^n} }$

$= \ \textgreater \ \frac{ \frac{(ab - 1)^n(ab + 1)^m}{ b^{m + n} } }{ \frac{(ab + 1)^m (ab-1)^n}{ a^{m+n} } }$

$= \ \textgreater \ \frac{(ab + 1)^m(ab-1)^n a^{m + n} }{ b^{m + n} (ab + 1)^m(ab - 1)^n}$

$= \ \textgreater \ \frac{ a^{m + n} }{ b^{m + n} }$

$= \ \textgreater \ ( \frac{a}{b}) ^{m + n}$



Hope this helps!