Show that

Question:

Show that

$\frac{\left(a+\frac{1}{b}\right)^{m} \times\left(a-\frac{1}{b}\right)^{n}}{\left(b+\frac{1}{a}\right)^{m} \times\left(b-\frac{1}{a}\right)^{n}}=\left(\frac{a}{b}\right)^{m+n}$

 

Solution:

$=\frac{\left(\frac{a b+1}{b}\right)^{m} \times\left(\frac{a b-1}{b}\right)^{n}}{\left(\frac{a b+1}{a}\right)^{m} \times\left(\frac{a b+1}{a}\right)^{n}}$

$=\left(\frac{a}{b}\right)^{m} \times\left(\frac{a}{b}\right)^{n}$

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

Hence, LHS = RHS

 

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