Question

Make r the subject of the formula t=r-3}" alt="\frac{r}{r-3}" align="absmiddle" class="latex-formula">

Answer 1

Answer:

$r=\frac{3t}{t-1}$

Step-by-step explanation:

So we have the formula:

$t=\frac{r}{r-3}$

And we want to make r the subject of the formula.

So, first, let's multiply both sides by (r-3). The right will cancel. So:

$t(r-3)=r$

Distribute the t:

$rt-3t=r$

Subtract rt from both sides. The left cancels:

$-3t=r-rt$

Factor out an r from the right:

$-3t=r(1-t)$

Divide both sides by (1-t). The right cancels:

$\frac{-3t}{1-t}=r$

Simplify the negatives:

$\frac{3t}{t-1}=r$

Flip:

$r=\frac{3t}{t-1}$

And we're done!