Question

please solve this,its a request i will mark brainliest whose answer is with step wise step explanation

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Answer 1

Solution

$\tt \to \: \dfrac{ \sqrt{ {a}^{2} - b {}^{2} } + a }{ \sqrt{ {a}^{2} + {b}^{2} } + b } \div \dfrac{ \sqrt{ {a}^{2} + {b}^{2} } - b}{a - \sqrt{ {a}^{2} - {b}^{2} } }$

$\tt \to \: \dfrac{ \sqrt{ {a}^{2} - b {}^{2} } + a }{ \sqrt{ {a}^{2} + {b}^{2} } + b } \times \dfrac{a - \sqrt{ {a}^{2} - {b}^{2} } }{ \sqrt{ {a}^{2} - {b}^{2} } - b}$

Now We are using identities

$\tt \to( {a} + b)(a - b) = {a}^{2} - {b}^{2}$

We get

$\tt \to \: \dfrac{(a)^{2} - ( \sqrt{ {a}^{2} - {b}^{2} }) {}^{2} } {( \sqrt{ {a}^{2} + {b}^{2}})^{2} - (b)^{2} }$

$\tt \to \: \dfrac{ {a}^{2} - {a}^{2} + {b}^{2} }{ {a}^{2} + {b}^{2} - {b}^{2} }$

$\tt \to \: \dfrac{ {b}^{2} }{ {a}^{2} }$

Answer

$\tt \to \: \dfrac{ {b}^{2} }{ {a}^{2} }$

Answer 2

Refers to attachment..................

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