Question

Simplify:(x/y+y/x-1)+(x^2/y^2-x/y+1)​

Answer 1

`= \frac{ - xy + {y}^(4) + {y}^(3) + {x}^(3)y + {x}^(3) - {x}^(2) }{x {y}^(3) + {xy}^(2) - {y}^(3) - {y}^(2) }`

Explanation:

`( (x)/(y) + (y)/(x - 1) ) + ( \frac{ {x}^(2) }{ {y}^(2) } - (x)/(y + 1) )`

`\frac{xy * (x - 1) * (y + 1) + {y}^(3) * (y + 1) + {x}^(2) * (x - 1) * (y + 1) - {xy}^(2) * (x - 1)}{ {y}^(2) * (x - 1) * (y + 1)}`

`\frac{( {x}^(2) y - xy) * (y + 1) + {y}^(4) + {y}^(3) + ( {x}^(3) - {x}^(2) ) * (y + 1) - {x}^(2) {y}^(2) + {xy}^(2) }{( {xy}^(2) - {y}^(2) ) * (y + 1)}`

`\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) ) }`

`= \frac{ - xy + {y}^(4) + {y}^(3) + {x}^(3)y + {x}^(3) - {x}^(2) }{x {y}^(3) + {xy}^(2) - {y}^(3) - {y}^(2) }`

Answer 2

2

Explanation: