Answer
$r=-14$
Work Step by Step
Given:$\frac{2r}{r-4}-\frac{4}{r+5}=2$
$\dfrac{2r}{r-4}=2+\dfrac{4}{r+5}$
$\dfrac{2r}{r-4}=\dfrac{2r+10+4}{r+5}$
Apply cross products.
$2r(r+5)=(2r+14)(r-4)$
$2r^2+10r=2r^2-8r+14r-56$
$10r+8r-14r+56=0$
Hence, $r=-14$
