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

User Denis Priebe
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Math Topic : Algebraic Simplification
Simplify. (x+y)/(x^2y)-(x-2y)/(xy^2)-example-1
User JanBrus
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Answer:


{ \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) }}

User Jithesh Kt
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