Answer:
[tex]\displaystyle r=\frac{3t}{t-1}[/tex]
Step-by-step explanation:
We are given the formula:
[tex]\displaystyle t=\frac{r}{r-3}[/tex]
And we are asked to make r the subject of the formula.
We can multiply both sides by r - 3. This reduces the denominator on the right-hand side:
[tex]t(r-3)=r[/tex]
Distribute:
[tex]rt-3t=r[/tex]
Subtracting rt from both sides yields:
[tex]-3t=r-rt[/tex]
Factoring:
[tex]-3t=r(1-t)[/tex]
Divide and simplify:
[tex]\displaystyle \begin{aligned} r & = \frac{-3t}{1-t} \\ \\ & = \frac{3t}{t-1}\end{aligned}[/tex]
In conclusion:
[tex]\displaystyle r=\frac{3t}{t-1}[/tex]
