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andre [41]
2 years ago
6

50points+brainliest for the one who solved this.It's not a homework but I am curious​

Mathematics
1 answer:
4vir4ik [10]2 years ago
4 0

Answer:

  • 1/xy

Step-by-step explanation:

<u>Simplify the numerator:</u>

  • (2x - y)/(2x + y) + (2x + y)/(3y - 6x) + 8xy/(12x² - 3y²) =
  • (2x - y)/(2x + y) - (2x + y)/3(2x - y) + 8xy/3(2x + y)(2x - y) =
  • [3(2x - y)² - (2x + y)² + 8xy] / [3(2x + y)(2x - y)] =
  • [12x² - 12xy + 3y² - 4x² - 4xy - y² + 8xy] / [3(2x + y)(2x - y)] =
  • [8x² - 8xy + 2y²] / [3(2x + y)(2x - y)] =
  • 2{2x - y)² / [3(2x + y)(2x - y)] =
  • 2(2x - y) / [3(2x + y)]

<u>Simplify the denominator:</u>

  • (4x²y - 2xy²) / (6x + 3y) =
  • 2xy(2x - y) / [3(2x + y)]

<u>Now simplify the remainder of the expression:</u>

  • 2(2x - y) / [3(2x + y)] × [3(2x + y)]/[2xy(2x - y}] =
  • 1/xy
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