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Rearrange the formula to make [tex]$r$[/tex] the subject.

[tex]t = \frac{r}{r-3}[/tex]

Sagot :

GinnyAnswer
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]
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