Answer:
Step-by-step explanation:
Simplify the numerator:
- (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)]
Simplify the denominator:
- (4x²y - 2xy²) / (6x + 3y) =
- 2xy(2x - y) / [3(2x + y)]
Now simplify the remainder of the expression:
- 2(2x - y) / [3(2x + y)] × [3(2x + y)]/[2xy(2x - y}] =
- 1/xy
