Question

Correct Answer pls....

Answer 1

Step-by-step explanation:

We have,

$\frac{ \sqrt{ {a}^{2} - {b}^{2} } + a}{ \sqrt{ {a}^{2} + {b}^{2} } + b} \div \frac{ \sqrt{ {a}^{2} + {b}^{2} } - b}{a - \sqrt{ {a}^{2} - {b}^{2} } }$

$= \frac{ \sqrt{ {a}^{2} - {b}^{2} } + a}{ \sqrt{ {a}^{2} + {b}^{2} } + b} \times \frac{a - \sqrt{ {a}^{2} - {b}^{2} } }{\sqrt{ {a}^{2} + {b}^{2} } - b}$

$= \frac{ \{\sqrt{ {a}^{2} - {b}^{2} } + a \} \{ a - \sqrt{ {a}^{2} - {b}^{2} } \}}{ \{\sqrt{ {a}^{2} + {b}^{2} } + b \} \{ \sqrt{ {a}^{2} + {b}^{2} } - b \} }$

$= \frac{ (a) ^{2} - (\sqrt{ {a}^{2} - {b}^{2} })^{2} }{ (\sqrt{ {a}^{2} + {b}^{2} }) ^{2} - (b)^{2} }$

$= \frac{ a^{2} - {a}^{2} + {b}^{2} }{ {a}^{2} + {b}^{2} - b^{2} }$

$= \frac{ {b}^{2} }{ {a}^{2} }$