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The given equation is:

\[
\frac{1}{p} + \frac{1}{q} = \frac{1}{f}
\]

We need to solve for \( q \).

### Steps to solve for \( q \):

1. Start by subtracting \(\frac{1}{p}\) from both sides of the equation:

\[
\frac{1}{q} = \frac{1}{f} - \frac{1}{p}
\]

2. Combine the fractions on the right-hand side:

\[
\frac{1}{q} = \frac{p - f}{fp}
\]

3. Finally, take the reciprocal of both sides to solve for \( q \):

\[
q = \frac{fp}{p - f}
\]

### Final Answer:
\[
q = \frac{fp}{p - f}
\]

Would you like any further details or explanations?

Here are some related questions you might consider:

1. What would happen if \( p = f \)?
2. How would you solve the equation if you needed to solve for \( p \) instead of \( q \)?
3. Can this equation be rearranged to find \( f \) directly?
4. How does this equation relate to optical systems, such as lenses or mirrors?
5. What are the physical interpretations of \( p \), \( q \), and \( f \) in this context?

**Tip:** When solving equations involving fractions, it's often helpful to find a common denominator or take reciprocals to simplify the process.

Consider the equation: \( \frac{1}{p} + \frac{1}{q} = \frac{1}{f} \). Solve for \( q \).

Learn how to solve the rational equation \( \frac{1}{p} + \frac{1}{q} = \frac{1}{f} \) by isolating \( q \) and applying algebraic techniques. This problem is ideal for students in Grades 9-12, covering key concepts in algebra.

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