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2014-11-01T15:39:10+05:30

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[( \frac{ x^{a/a-b} }{ x^{a/a+b} } )/( \frac{ x^{b/b-a} }{ x^{b/b+a} } )] ^{a+b} \\  \\ =[(x^{ \frac{a}{a-b} - \frac{a}{a+b} })/( x^{ \frac{b}{b-a} - \frac{b}{b+a} } )] ^{a+b} \\  \\ =[(x^{ \frac{a^{2}+ab-a^{2}+ab}{a^{2}-b^{2}}  })/( x^{ \frac{b^{2}+ab-b^{2}+ab }{(b-a)(b+a)}  } )] ^{a+b} \\  \\ =[(x^{ \frac{2ab}{a^{2}-b^{2}}  })/( x^{ \frac{2ab }{(b^{2}-a^{2}}  } )] ^{a+b} \\  \\ =(x^{ \frac{(2ab)(a+b)}{a^{2}-b^{2}}  })/( x^{ \frac{(2ab)(a+b) }{(b^{2}-a^{2}}  } )

 =(x^{ \frac{2ab}{a-b}  })/( x^{ \frac{2ab}{b-a}  } ) \\  \\ =x^{2ab( \frac{1}{a-b} - \frac{1}{b-a} )} \\  \\ =x^{2ab( \frac{1}{a-b} + \frac{1}{a-b} )} \\  \\ =x^{ \frac{4ab}{a-b}}

Note: (b/b+a) has been used instead of (b/b+1) as it is easy to do. if (b/b+1) is used, the expression would be a bit long, but it can be done. 
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