# How do you solve (5k + 5)/(3k^2) = (k - 4)/(3k^2) + 1/k^2 and find any extraneous solutions?

May 28, 2016

$k = - \frac{3}{2}$

#### Explanation:

Reducing to the same denominator

$\frac{5 k + 5}{3 {k}^{2}} = \frac{k - 4}{3 {k}^{2}} + \frac{3}{3 {k}^{2}}$

or

$\frac{5 k + 5}{3 {k}^{2}} - \frac{k - 4}{3 {k}^{2}} - \frac{3}{3 {k}^{2}} = 0$

or

$\frac{\left(5 k + 5\right) - \left(k - 4\right) - 3}{3 {k}^{2}} = 0$

or

$\frac{4 k + 6}{3 {k}^{2}} = 0$

Solving for $k$ we obtain $k = - \frac{3}{2}$