To solve for \( T \) from the equation \( e = \frac{T}{T - U} \), follow these steps:

### Step 1: Multiply both sides of the equation by \( T - U \) to eliminate the fraction:
\[
e(T - U) = T
\]

### Step 2: Distribute \( e \) on the left-hand side:
\[
eT - eU = T
\]

### Step 3: Move all terms involving \( T \) to one side of the equation:
\[
eT - T = eU
\]

### Step 4: Factor out \( T \) from the left-hand side:
\[
T(e - 1) = eU
\]

### Step 5: Solve for \( T \):
\[
T = \frac{eU}{e - 1}
\]

Thus, the solution is:
\[
T = \frac{eU}{e - 1}
\]

Would you like further clarification on any step, or more details? 

Here are 5 related questions to extend this problem:
1. How would the equation change if the variable \( e \) represented an exponential expression?
2. Can you solve for \( U \) instead of \( T \) in the same equation?
3. How does the solution change if \( e = 1 \)?
4. What happens to \( T \) as \( e \) approaches infinity?
5. How can this equation be used in practical applications, such as physics or economics?

**Tip**: Always double-check by substituting the solution back into the original equation to ensure accuracy.

Learn how to solve for T from the equation e = T / (T - U) with a detailed step-by-step solution. This problem explores rational equations and algebraic manipulation, suitable for students in Grades 9-11.

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