Math, asked by Devil8233, 5 hours ago

please solve it urgently and correctly​

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Answered by TheGodWishperer
3

Solution:-

 \LARGE\mathtt{  \: \: \: \: \: \: \: \: \: \: \: \:\frac{ {a}^{ - 1} }{ {a}^{ - 1} +  {b}^{ - 1}   } +  \frac{ {a}^{ - 1} }{ {a}^{ - 1}  -   {b}^{ - 1}    }}

\LARGE \mathtt{ : \rightarrow \: \: \: \: \: \: \: \: \: \: \: \:\frac{ \frac{1}{a} }{\frac{1}{a} +  \frac{1}{b}   }  + \frac{ \frac{1}{a} }{\frac{1}{a}  -   \frac{1}{b} }}

\LARGE\mathtt{: \rightarrow \: \: \: \: \: \:  \: \: \: \: \: \:\frac{ \frac{1}{a} }{\frac{b + a}{ab}   }  + \frac{ \frac{1}{a} }{\frac{b - a}{ab}  }}

\LARGE\mathtt{: \rightarrow  \: \: \: \: \: \:  \: \: \: \: \: \: \frac{b}{b + a} + \frac{ b }{  b - a}}

\LARGE\mathtt{ : \rightarrow \: \: \: \: \: \:   \: \: \: \: \: \:\frac{b(b - a) + b(b + a)}{(b + a)(b - a)}}

\LARGE\mathtt{ : \rightarrow  \: \: \: \: \: \:  \: \: \: \: \: \:\frac{ {b}^{2}  - ba +  {b}^{2} + ba }{(b + a)(b - a)}}

\LARGE\mathtt{: \rightarrow   \: \: \: \: \: \:  \: \: \: \: \: \:\frac{ 2{b}^{2}   }{(b + a)(b - a)}}

 \LARGE: \rightarrow\mathtt{   \: \: \: \: \: \:  \: \: \: \: \: \:\frac{ 2{b}^{2}   }{ {b}^{2}  -  {a}^{2} }}

Hence proved

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