Question

Solve a Rational Equation for a Specific Variable.

In the following exercises, solve.

$r=\frac{s}{3-t}$for$t$.

Short answer

The solution is $t=\frac{3r-s}{r}$

Step-by-step solution

Step 1. Given  

The given rational equation is $r=\frac{s}{3-t}$.

Step 2. To find 

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

Step 3. Calculation  

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

$$\begin{gathered} r=\frac{s}{3-t} \\ r\left(3-t\right)=s \\ 3r-rt=s \\ 3r=s+rt \\ 3r-s=rt \\ \frac{3r-s}{r}=\frac{rt}{r} \\ \frac{3r-s}{r}=t \\ t=\frac{3r-s}{r} \end{gathered}$$