Question

PLS HELP ME IN THIS ANSWER PLS SHOW STEP BY STEP AND KEEP IT SIMPLE THANK YOU​

Answer 1

Step-by-step explanation:

$\frac{ {x}^{ - 1} + {y}^{ - 1} }{ {x}^{ - 1} } + \frac{ {x}^{ - 1} - {y}^{ - 1} }{ {y}^{ - 1} } \\ \\ = \frac{ \frac{1}{x} + \frac{1}{y} }{ \frac{1}{x} } + \frac{ \frac{1}{x} - \frac{1}{y} }{ \frac{1}{y} } \\ \\ = \frac{ \frac{y + x}{xy} }{ \frac{1}{x} } + \frac{ \frac{ y - x}{xy} }{ \frac{1}{y} } \\ \\ = \frac{y + x}{xy} \div \frac{1}{x} + \frac{y - x}{xy} \div \frac{1}{y} \\ \\ = \frac{y + x}{xy} \times x + \frac{y - x}{xy} \times {y} \\ \\ = \frac{y + x}{y} + \frac{y - x}{x} \\ \\ = \frac{(y + x)x}{xy} + \frac{ (y - x)y}{xy} \\ \\ = \frac{(y + x)x + (y - x)y}{xy} \\ \\ = \frac{xy + {x}^{2} + {y}^{2} - xy }{xy} \\ \\ = \frac{ {x}^{2} + {y}^{2} }{xy}$