Sure! Let's rearrange the formula to make \( r \) the subject.
The given formula is:
[tex]\[ t = \frac{r}{r - 3} \][/tex]
Here are the steps to rearrange it:
1. Multiply both sides by the denominator \( (r - 3) \) to get rid of the fraction:
[tex]\[ t(r - 3) = r \][/tex]
2. Distribute \( t \) on the left side:
[tex]\[ tr - 3t = r \][/tex]
3. Move all terms involving \( r \) to one side. Subtract \( r \) from both sides:
[tex]\[ tr - r = 3t \][/tex]
4. Factor \( r \) out from the left side:
[tex]\[ r(t - 1) = 3t \][/tex]
5. Divide both sides by \( (t - 1) \) to isolate \( r \):
[tex]\[ r = \frac{3t}{t - 1} \][/tex]
So the formula rearranged to make \( r \) the subject is:
[tex]\[ r = \frac{3t}{t - 1} \][/tex]
