Question

Solve a Rational Equation for a Specific Variable.

In the following exercises, solve.

$\frac{m+3}{n-2}=\frac{4}{5}$for$n$.

Short answer

The solution is $n=\frac{5m+23}{4}$.

Step-by-step solution

Step 1. Given 

The given rational equation is $\frac{m+3}{n-2}=\frac{4}{5}$.

Step 2. To find  

We have to solve the given rational equation for$n$.

Step 3. Calculation  

We cross multiply, then solve the equation for$n$.

$$\begin{gathered} \frac{m+3}{n-2}=\frac{4}{5} \\ 5\left(m+3\right)=4\left(n-2\right) \\ 5m+15=4n-8 \\ 5m+15+8=4n-8+8 \\ 5m+23=4n \\ \frac{5m+23}{4}=\frac{4n}{4} \\ \frac{5m+23}{4}=n \\ n=\frac{5m+23}{4} \end{gathered}$$