# How do you solve v/(v-9)=10/6?

Aug 19, 2016

$v = 22.5$
Get rid of the denominators by multiplying both sides by $\textcolor{red}{6 \left(v - 9\right)}$ Then solve for $v$

#### Explanation:

By multiplying both sides by the LCD of both denominators, the denominators are eliminated and the problem is simplified.

$\textcolor{red}{6 \left(v - 9\right)} \times \frac{v}{v - 9} = \textcolor{red}{6 \left(v - 9\right)} \times \frac{10}{6}$

Because $\frac{\left(v - 9\right)}{\left(v - 9\right)} = 1 \mathmr{and} \frac{6}{6} = 1$ this allows us to cancel.

$\textcolor{red}{6 \cancel{\left(v - 9\right)}} \times \frac{v}{\cancel{v - 9}} = \textcolor{red}{\cancel{6} \left(v - 9\right)} \times \frac{10}{\cancel{6}}$

This leaves the equation as

$6 \left(v\right)$ = $\left(v - 9\right) \times 10$

Multiplying across the parenthesis gives

$6 v = 10 v - 90$

Subtract $10 v$ from both sides. (Remember when you're trying to solve or find something always work backwards. PE SAD M -4

Do Parathesis and exponent first then do subtraction and addition from left to right, before doing division and multiplication from left to right.

$6 v - 10 v = 10 v - 10 v - 90$

this leaves

$- 4 v = - 90$

Now divide both sides by $- 4$ to solve for $v$

$\frac{- 4 v}{-} 4 = \frac{- 90}{- 4}$

this gives

$v = + 22.5$