Question

Упростите, пожалуйста
$(\frac{{d}^{3} -8}{{d}^2-4} -\frac{6d}{d+2} ):(1-\frac{4}{d+2} )^{2}$

Answer 1

$\left(\frac{(d-2)(d^2+2d+4)}{(d-2)(d+2)}-\frac{6d}{d+2}\right):\left(\frac{d+2-4}{d+2}\right)^2=\frac{d^2+2d+4-6d}{d+2}\cdot \frac{(d+2)^2}{(d-2)^2}=(d^2-4d+4)\cdot \frac{d+2}{(d-2)^2}=(d-2)^2\cdot\frac{d+2}{(d-2)^2}=d+2$