Question

y+6 y+2 5
___ - ____ + ____ - спростити вираз
4y+8 4y-8 y^2 -4

Answer 1

$\frac{y + 6}{4y + 8} - \frac{y + 2}{4y - 8} + \frac{5}{ {y}^{2} - 4 } = \frac{y + 6}{4(y + 2)} - \frac{y + 2}{4(y - 2)} + \frac{5}{(y - 2)(y + 2)} = \frac{ (y + 6)(y + 2)}{4(y + 2)(y - 2)} - \frac{(y + 2) ^{2} }{4(y - 2)(y + 2)} - \frac{20}{4(y - 2)(y + 2)} = \frac{ {y}^{2} + 6y + 2y + 12 - {y}^{2} - 4y - 4 - 20 }{4(y - 2)( y + 2)} = \frac{4y - 12}{4(y - 2)(y + 2)} = \frac{4(y - 3)}{4(y - 2)(y + 2)} = \frac{y - 3}{(y - 2)(y + 2)}$