# How do you solve n/(n-3)=2/3?

May 10, 2017

Cross multiplication. Answer: $n = - 6$

#### Explanation:

First, we can cross multiply to get $n$ out of a fraction:
$3 n = 2 \left(n - 3\right)$

We can use the distributive property on the right-hand side:
$3 n = 2 n - 6$

By subtracting $2 n$ from both sides, we get $n$ terms on one side:
$n = - 6$ which is our answer

May 10, 2017

See a solution process below:

#### Explanation:

First, multiply each side of the equation by $\textcolor{red}{\left(n - 3\right)} \textcolor{b l u e}{3}$ to eliminate the fractions while keeping the equation balanced. $\textcolor{red}{\left(n - 3\right)} \textcolor{b l u e}{3}$ is the Lowest Common Denominator of the two fractions:

$\textcolor{red}{\left(n - 3\right)} \textcolor{b l u e}{3} \times \frac{n}{n - 3} = \textcolor{red}{\left(n - 3\right)} \textcolor{b l u e}{3} \times \frac{2}{3}$

$\cancel{\textcolor{red}{\left(n - 3\right)}} \textcolor{b l u e}{3} \times \frac{n}{\textcolor{red}{\cancel{\textcolor{b l a c k}{n - 3}}}} = \textcolor{red}{\left(n - 3\right)} \cancel{\textcolor{b l u e}{3}} \times \frac{2}{\textcolor{b l u e}{\cancel{\textcolor{b l a c k}{3}}}}$

$3 n = 2 \left(n - 3\right)$

Next, expand the terms in parenthesis on the right side of the equation:

$3 n = \left(2 \times n\right) - \left(2 \times 3\right)$

$3 n = 2 n - 6$

Now, subtract $\textcolor{red}{2 n}$ from each side of the equation to solve for $n$ while keeping the equation balanced:

$- \textcolor{red}{2 n} + 3 n = \textcolor{red}{2 n} + 2 n - 6$

$\left(- \textcolor{red}{2} + 3\right) n = 0 - 6$

$1 n = - 6$

$n = - 6$