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

### Step 1: Isolate \( \frac{x}{a} \)
Subtract \( \frac{c}{b} \) from both sides of the equation:

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

### Step 2: Simplify the right-hand side
Find a common denominator on the right-hand side. The common denominator between 1 and \( \frac{c}{b} \) is \( b \), so rewrite 1 as \( \frac{b}{b} \):

\[
\frac{x}{a} = \frac{b}{b} - \frac{c}{b} = \frac{b - c}{b}
\]

### Step 3: Solve for \( x \)
Multiply both sides of the equation by \( a \) to solve for \( x \):

\[
x = a \cdot \frac{b - c}{b}
\]

### Final answer:
\[
x = \frac{a(b - c)}{b}
\]

Would you like a detailed explanation of any step?

Here are 5 related questions:
1. What happens if \( b = c \)?
2. How would the solution change if the equation was \( \frac{x}{a} - \frac{c}{b} = 1 \)?
3. Can this approach be used for solving systems of linear equations?
4. How does multiplying both sides by the denominator affect the solution?
5. What are some real-life applications of such rational equations?

**Tip**: Always simplify equations by isolating the variable and using common denominators for fractions.

Learn how to solve the rational equation x/a + c/b = 1 for x. This solution covers key algebraic concepts like isolating variables, finding common denominators, and solving linear equations. Suitable for students in Grades 8-10.

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