Solve for r in the following equation 1r−1 1 r − 1 + 2r+1 2 r + 1 = 3r

Solve for r in the following equation $\frac{1}{r-1}$ + $\frac{2}{r+1}$ = $\frac{3}{r}$

Answer Details

$\frac{1}{r-1}$ + $\frac{2}{r+1}$ = $\frac{3}{r}$
Multiply through by r(r -1) which is the LCM
= (r)(r + 1) + 2(r)(r - 1)
= 3(r - 1)(r + 1)
= r2 + r + 2r2 - 2r
3r2 - 3 = 3r2
r = 3r2 - 3
-r = -3
∴ r = 3