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To make \( a \) the subject of the equation, we start from the given equation:

\[
P = \frac{n^2 + a}{n + a}
\]

### Step-by-step solution:

1. **Multiply both sides by \( n + a \):**

\[
P(n + a) = n^2 + a
\]

2. **Distribute \( P \) on the left-hand side:**

\[
Pn + Pa = n^2 + a
\]

3. **Move all terms involving \( a \) to one side and the rest to the other:**

\[
Pa - a = n^2 - Pn
\]

4. **Factor out \( a \) on the left-hand side:**

\[
a(P - 1) = n^2 - Pn
\]

5. **Solve for \( a \):**

\[
a = \frac{n^2 - Pn}{P - 1}
\]

Thus, the expression for \( a \) is:

\[
a = \frac{n^2 - Pn}{P - 1}
\]

Would you like any further explanation or details?

Here are 5 related questions you might find interesting:
1. How can we use this formula for specific values of \( n \) and \( P \)?
2. What happens to the equation if \( P = 1 \)?
3. How can we verify that \( a \) is correctly isolated?
4. What is the behavior of \( a \) as \( P \) approaches 1 from both sides?
5. How does this equation relate to quadratic functions?

**Tip:** When isolating a variable, make sure to carefully factor and handle any common terms to simplify the solution.

Make a the subject of the equation: P = (n^2 + a) / (n + a)

This tutorial explains how to make 'a' the subject of the equation P = (n^2 + a) / (n + a). Follow the detailed steps to understand algebraic manipulation and inverse operations. Ideal for students in Grades 9-12.

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