Answer
$r = -1$
Work Step by Step
$2/r + 1/(r^2) + (r^2+r)/(r^3) = 1/r$
$r^3*(2/r + 1/(r^2) + (r^2+r)/(r^3) = 1/r)$
$2*r^3/r + 1*r^3/(r^2) + r^3*(r^2+r)/(r^3) = (1/r)*r^3$
$2*r^2 + r + (r^2+r) = r^2$
$2r^2 +r + r^2 +r = r^2$
$2r^2 + 2r = 0$
$2r(r+1)=0$
$2r=0$
$r=0$ (we can't have zero in the denominator, so this answer is invalid)
$r+1=0$
$r=-1$
$r=-1$
$2/r + 1/(r^2) + (r^2+r)/(r^3) = 1/r$
$2/(-1) + 1/((-1)^2) + ((-1)^2+(-1))/((-1)^3) = 1/(-1)$
$-2 +(1/1) +(1-1)/-1 = -1$
$-2 + 1 +0 = -1$
$-2+1+0 = -1$
$-1 =-1$
