Question

(x / y ) x- y + ( y / x ) y - x = ?
solution batado ​

Answer 1

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Answer 2

$( \frac{x}{y} )x - y + ( \frac{y}{x} )y - x \\ \\ = \frac{ {x}^{2} }{y} - y + \frac{ {y}^{2} }{x} - x \\ \\ = \frac{ (({x}^{2})-( y \times y)) }{y} + \frac{ {y}^{2} }{x} - x \\ \\ = \frac{ {x}^{2} - {y}^{2} }{y} + \frac{{y}^{2} }{x} - x \\ \\ = \frac{ {x}^{2} - {y}^{2} }{y} + \frac{(({y}^{2}) - (x \times x))}{x} \\ \\ = \frac{ {x}^{2} - {y}^{2} }{y} + \frac{{y}^{2} - {x}^{2} }{x} \\ \\ = \frac{x( {x}^{2} - {y}^{2}) + y( {y}^{2} - {x}^{2}) }{(y \times x)} \\ \\ = \green{\boxed{ \frac{ {x}^{3} - x {y}^{2} + {y}^{3} - {x}^{2} y }{xy}}}$