Question

Упростите выражение $\frac{4y}{ y^{2}-4 } - \frac{2}{y-2}$

Answer 1

$\frac{4y}{ y^{2}-4 } - \frac{2}{y-2} = \frac{4y}{ (y-2)(y+2) } - \frac{2}{y-2} =\frac{4y}{ (y-2)(y+2) } - \frac{2(y+2)}{(y-2)(y+2)} = \\ =\frac{4y-2y-4}{(y-2)(y+2)} =\frac{2y-4}{(y-2)(y+2)} =\frac{2(y-2)}{(y-2)(y+2)} = \frac{2}{y+2}$