Question

Make r the subject of the formula t=
`(r)/(r-3)`

Answer 1

`\displaystyle r=(3t)/(t-1)`

Explanation:

We are given the formula:

`\displaystyle t=(r)/(r-3)`

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:

`t(r-3)=r`

Distribute:

`rt-3t=r`

Subtracting rt from both sides yields:

`-3t=r-rt`

Factoring:

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

Divide and simplify:

`\displaystyle \begin{aligned} r & = (-3t)/(1-t) \\ \\ & = (3t)/(t-1)\end{aligned}`

In conclusion:

`\displaystyle r=(3t)/(t-1)`