Question

$x - \frac{xy}{x + y} + \frac{x {}^{3} }{x {}^{2} - y {}^{2} }$
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Answer 1

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