Question

plss simplify the following​

Answer 1

Answer:

(x/y)²

Step-by-step explanation:

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