Question

Simplify. (x+y)/(x^2y)-(x-2y)/(xy^2)

Answer 1

Math Topic : Algebraic Simplification

Answer 2

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

Find the LCM of denominators: x²y²

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

Simplify further:

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