Question

pls tell how to solve fast pls pls ​

Answer 1

Answer:

x²/y²

Step-by-step explanation:

$\frac{ \sqrt{ {x}^{2} + {y}^{2} } - y }{x - \sqrt{ {x}^{2} - {y}^{2} } } \div \frac{ \sqrt{ {x}^{2} - {y}^{2} } + x}{ \sqrt{ {x}^{2} + {y}^{2} } + y } \\ = \frac{ \sqrt{ {x}^{2} + {y}^{2} } - y }{x - \sqrt{ {x}^{2} - {y}^{2} } } \times \frac{ \sqrt{ {x}^{2} + {y}^{2} } + y}{ \sqrt{ {x}^{2} - {y}^{2} } + x} \\ = \frac{ (\sqrt{ {x}^{2} + {y}^{2} } - y ) \times(\sqrt{ {x}^{2} + {y}^{2} } + y ) }{(x - \sqrt{ {x}^{2} + {y}^{2} } ) \times( x + \sqrt{ {x}^{2} - {y}^{2} } ) } \\ = \frac{ {( \sqrt{ {x}^{2} + {y}^{2} })}^{2} - {y}^{2} }{ {x}^{2} - {( \sqrt{ {x}^{2} - {y}^{2} } })^{2} } \\ = \frac{ {x }^{2} + {y}^{2} - {y}^{2} }{ {x}^{2} - ( {x}^{2} - {y}^{2} ) } \\ = \frac{ {x}^{2} }{ {x}^{2} - {x}^{2} + {y}^{2} } \\ = \frac{ {x}^{2} }{ {y}^{2} }$

Note:-

Formula used in this question--

(a+b)(a-b) = (a)² - (b)²