# How do you solve \frac { v - 6} { v - 4} = \frac { v } { v + 1}?

Mar 12, 2018

$v = - 6.$

#### Explanation:

$\frac{v - 6}{v - 4} = \frac{v}{v + 1}$

or, $\left(v - 6\right) \left(v + 1\right) = v \left(v - 4\right)$

or, ${v}^{2} - 5 v - 6 = {v}^{2} - 4 v$

Cancelling the ${v}^{2}$ on both sides,
we have:
$- 5 v - 6 = - 4 v$

Simplifying further,

$- v - 6 = 0$

or, $- v = 6$
Thus, we have, $v = - 6$

Plugging in the value of $v$ in the equation,
Left hand side is:
$\frac{v - 6}{v - 4} = \frac{- 6 - 6}{- 6 - 4} = \frac{- 12}{-} 10 = \frac{6}{5}$

Plugging in the value of $v$ in the Right hand side:

$\frac{v}{v + 1} = - \frac{6}{- 6 + 1} = \frac{- 6}{-} 5 = \frac{6}{5}$

Thus, $L H S = R H S$ in the equation.

Hope this helps!!