Answer:
[tex] = \frac{ - xy + {y}^{4} + {y}^{3} + {x}^{3}y + {x}^{3} - {x}^{2} }{x {y}^{3} + {xy}^{2} - {y}^{3} - {y}^{2} } [/tex]
Step-by-step explanation:
[tex]( \frac{x}{y} + \frac{y}{x - 1} ) + ( \frac{ {x}^{2} }{ {y}^{2} } - \frac{x}{y + 1} )[/tex]
[tex] \frac{xy \times (x - 1) \times (y + 1) + {y}^{3} \times (y + 1) + {x}^{2} \times (x - 1) \times (y + 1) - {xy}^{2} \times (x - 1)}{ {y}^{2} \times (x - 1) \times (y + 1)} [/tex]
[tex]\frac{( {x}^{2} y - xy) \times (y + 1) + {y}^{4} + {y}^{3} + ( {x}^{3} - {x}^{2} ) \times (y + 1) - {x}^{2} {y}^{2} + {xy}^{2} }{( {xy}^{2} - {y}^{2} ) \times (y + 1)}[/tex]
[tex] \frac{ {x}^{2} {y}^{2} + {x}^{2} y - {xy}^{2} - xy + {y}^{4} + {y}^{3} + {x}^{3} y + {x}^{3} - {x}^{2}y - {x}^{2} - {x}^{2} {y}^{2} + {xy}^{2} }{( {xy}^{3} + {xy}^{2} - {y}^{3} - {y}^{2} ) } [/tex]
[tex] = \frac{ - xy + {y}^{4} + {y}^{3} + {x}^{3}y + {x}^{3} - {x}^{2} }{x {y}^{3} + {xy}^{2} - {y}^{3} - {y}^{2} } [/tex]
