To solve the equation \( 3 + q^2 = \frac{g}{r} \) for \( g \), follow these steps:

### Step 1: Eliminate the denominator
Multiply both sides of the equation by \( r \) to remove the fraction:
\[
r(3 + q^2) = g
\]

### Step 2: Simplify
\[
g = r(3 + q^2)
\]

Thus, the solution for \( g \) is:
\[
g = r(3 + q^2)
\]

Let me know if you need further details!

Here are some related questions:
1. How would you solve for \( r \) in the same equation?
2. What happens if \( r = 0 \)? How would that change the solution?
3. How would you approach this if \( q^2 \) were negative?
4. What if you had \( 3q + q^2 \) instead of \( 3 + q^2 \)?
5. How do you find the derivative of \( g = r(3 + q^2) \) with respect to \( q \)?

**Tip**: When solving equations with fractions, it's often easiest to eliminate the fraction by multiplying through by the denominator.

Learn how to solve the rational equation 3 + q^2 = g/r for g with a clear step-by-step explanation. This problem covers key algebra concepts, including solving for variables in rational equations. Suitable for students in Grades 8-10.

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