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To make \( r \) the subject of the formula \( t = \frac{r}{r - 3} \), follow these steps:

### Step 1: Multiply both sides by \( r - 3 \)
\[
t(r - 3) = r
\]

### Step 2: Expand the left-hand side
\[
t \cdot r - 3t = r
\]

### Step 3: Move all terms involving \( r \) to one side
\[
t \cdot r - r = 3t
\]

### Step 4: Factor out \( r \) on the left-hand side
\[
r(t - 1) = 3t
\]

### Step 5: Solve for \( r \)
\[
r = \frac{3t}{t - 1}
\]

Thus, the formula for \( r \) is:
\[
r = \frac{3t}{t - 1}
\]

Would you like more details or have any other questions?

### Related Questions:
1. What happens to the value of \( r \) when \( t = 1 \)?
2. Can this equation have any restrictions on the values of \( t \)?
3. How would this process change if there were additional constants in the equation?
4. What if \( t = 0 \)? How does that affect \( r \)?
5. How can you apply this method to more complex rational equations?

### Tip:
Always check for values that make the denominator zero to avoid undefined results.

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

This detailed guide shows how to make r the subject in the equation t = r / (r - 3). Follow the step-by-step algebraic solution to rearrange the formula and solve for r. Suitable for high school students in Grades 10-12.

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