# How do you solve 8/9=(n+6)/n?

Aug 31, 2016

$n = - 54$

#### Explanation:

When we have 1 fraction equal to another we can use the method of $\textcolor{b l u e}{\text{cross-multiplication}}$ to solve.

This is performed as follows.

$\frac{\textcolor{b l u e}{8}}{\textcolor{red}{9}} = \frac{\textcolor{red}{n + 6}}{\textcolor{b l u e}{n}}$

Now cross-multiply (X) the values on either end of an 'imaginary' cross and equate them.

That is multiply the $\textcolor{b l u e}{\text{blue}}$ values together and the $\textcolor{red}{\text{red}}$ values together and equate them.

$\Rightarrow \textcolor{red}{9 \left(n + 6\right)} = \textcolor{b l u e}{8 n}$

distribute the bracket

$\Rightarrow 9 n + 54 = 8 n$

subtract 8n from both sides

$\Rightarrow 9 n - 8 n + 54 = \cancel{8 n} - \cancel{8 n} \Rightarrow n + 54 = 0$

subtract 54 from both sides

$\Rightarrow n + \cancel{54} - \cancel{54} = 0 - 54$

$\Rightarrow n = - 54$

Aug 31, 2016

$n = - 54$

#### Explanation:

$\left(\frac{8}{9}\right) - \left(\frac{n + 6}{n}\right) = 0$
Taking common denominator $9 \left(n + 1\right)$ we have:

$\frac{8 n - 9 \left(n + 6\right)}{9 n} = 0$
$9 n \ne 0$so $n \ne 0$
$= \frac{8 n - 9 n - 54}{9 n}$
$= \frac{- n - 54}{9 n} = 0$
When the fraction equals zero so its numerator will be zero
So,
$- n - 54 = 0$
$- n = 54$
therefore, $n = - 54$ accepted