To solve the equation \(\frac{1}{a} + b = \frac{c}{a}\) for \(a\), follow these steps:

1. Start by multiplying the entire equation by \(a\) to eliminate the denominators:
   \[
   a \cdot \frac{1}{a} + a \cdot b = a \cdot \frac{c}{a}
   \]
   This simplifies to:
   \[
   1 + ab = c
   \]

2. Next, isolate \(ab\) on one side of the equation:
   \[
   ab = c - 1
   \]

3. Finally, solve for \(a\) by dividing both sides by \(b\):
   \[
   a = \frac{c - 1}{b}
   \]

So, the solution for \(a\) is:
\[
a = \frac{c - 1}{b}
\]

Would you like further details or have any questions?

Here are five related questions:

1. How would you solve the equation if \(b = 0\)?
2. What happens if \(c = 1\) in the equation?
3. Can this equation be solved for \(b\) instead of \(a\)?
4. How would you solve for \(a\) if the original equation were \(\frac{1}{a} - b = \frac{c}{a}\)?
5. What are the implications if \(c < 1\) in this equation?

**Tip:** Always check the domain of your variables to ensure they don't cause division by zero.

Learn how to solve the equation 1/a + b = c/a for the variable a with a detailed step-by-step solution. This problem covers key algebraic concepts such as manipulating equations and isolating variables. Suitable for high school students studying algebra.

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