Show that- a - 1bm- a - 1bn b - 1am- b - 1an - abm - n

(a+1/b)^m× (a 1/b)^n/(b+1/a)^m× (b 1/a)^n=(a/b)^m+n (ab+1/b)^m× (ab 1/b)^n/(ba+1/a)^m× (ab 1/a)^n=(1/b)^m+n/(1/b)^m+1 ⇒ (a/b)^m+n ...

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Question

Show that: $\frac{{(a + \frac{1}{b})}^{m} \times {(a - \frac{1}{b})}^{n}}{{(b + \frac{1}{a})}^{m} \times {(b - \frac{1}{a})}^{n}} = {(\frac{a}{b})}^{m + n}$

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Show that :

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

m, \frac{a^{m + 1} + b^{m + 1}}{a^{m} + b^{m}}

^{'} a^{'}

^{'} b^{'}

a

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\frac{{(\frac{a}{b})}^{m}}{{(\frac{a}{b})}^{n}} = {(\frac{a}{b})}^{m - n}

\frac{a^{n} + b^{n}}{a^{n - 1} + b^{n - 1}}

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b

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