dmorgan51 dmorgan51
  • 11-07-2021
  • Mathematics
contestada

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

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MuzanKibutsuji MuzanKibutsuji
  • 11-07-2021
Math Topic : Algebraic Simplification
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Аноним Аноним
  • 11-07-2021

Answer:

[tex]{ \tt{ = \frac{(x + y)}{ {x}^{2}y } - \frac{(x - 2y)}{ {xy}^{2} } }} [/tex]

Find the LCM of denominators: x²y²

[tex]{ \tt{ = \frac{y(x + y) - x(x - 2y)}{ {x}^{2} {y}^{2} } }} \\ \\ = { \tt{ \frac{xy + {y}^{2} - {x}^{2} +2xy }{ {x}^{2} {y}^{2} } }}[/tex]

Simplify further:

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

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