Answer
The equation has one solution, -14.
Work Step by Step
$\frac{2r}{r-4}-2=\frac{4}{r+5}$
$(r-4)(r+5)(\frac{2r}{r-4}-2)=(r-4)(r+5)\frac{4}{r+5}$
$\frac{(r-4)(r+5)2r}{r-4}-2(r-4)(r+5)=(r-4)(r+5)\frac{4}{r+5}$
$2r(r+5)-2(r^2+r-20)=4(r-4)$
$2r^2+10r-2r^2-2r+40=4r-16$
$8r+40=4r-16$
$4r=-56$
$r=-14$
Check:
$-(2\times14)/(-14-4)-2=14/9-2=-4/9; 4/(-14+5)=-4/9$
The equation has one solution, -14.
