$$ \frac{1}{a}-\frac{1}{f}=\frac{1}{b}+\frac{1}{c} $$

The given equation is:

\[
\frac{1}{a} - \frac{1}{f} = \frac{1}{b} + \frac{1}{c}
\]

This equation contains four variables: $a$, $f$, $b$, and $c$. Depending on what you want to solve for, we can rearrange the terms. Let me show you how to solve for a specific variable, say $a$, as an example. To solve for $a$:

### Step-by-step Solution (Solving for $a$):
1. Start by rewriting the equation:
   \[
   \frac{1}{a} = \frac{1}{f} + \frac{1}{b} + \frac{1}{c}
   \]
2. Combine the terms on the right-hand side into a single fraction. To do that, find the least common denominator (LCD) of $f$, $b$, and $c$:
   \[
   \frac{1}{a} = \frac{bcf + acf + abf}{abc}
   \]
   
Would you like a more detailed explanation of solving this or another example using a different variable?

Here are five questions to expand on this:

1. How do you combine fractions with different denominators?
2. Can we simplify the equation if any variables are given as constants?
3. What happens if one of the denominators becomes zero?
4. How would you solve for $f$ instead of $a$?
5. Is there a physical interpretation for this equation in any field (e.g., optics)?

**Tip**: When solving for a variable, always isolate it step by step, keeping in mind how to manage fractions effectively.

This page provides a step-by-step solution to the equation 1/a - 1/f = 1/b + 1/c. Learn how to solve for different variables, apply the concept of least common denominators, and manage fractional equations. Suitable for students in Grades 9-12.

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