Find the following if a+b over a-b=c. 3a+3b over 2a-2b

We are given the equation:

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

Now, we need to find the expression:

\[
\frac{3a+3b}{2a-2b}
\]

### Step 1: Factor out common terms in the numerator and denominator.

\[
\frac{3a + 3b}{2a - 2b} = \frac{3(a + b)}{2(a - b)}
\]

### Step 2: Use the fact that \(\frac{a+b}{a-b} = c\).

This means that:

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

Thus, we can substitute \(c\) into the expression:

\[
\frac{3(a+b)}{2(a-b)} = \frac{3}{2} \cdot \frac{a+b}{a-b} = \frac{3}{2} \cdot c
\]

### Final Answer:

\[
\frac{3a + 3b}{2a - 2b} = \frac{3}{2}c
\]

Would you like further clarification on any step or details?

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Here are 5 related questions to expand this topic:

1. How do you manipulate algebraic fractions with complex terms?
2. What are common ways to simplify fractions like \(\frac{a+b}{a-b}\)?
3. Can you explain how to substitute expressions in equations?
4. How does factoring help in solving algebraic expressions?
5. What are other examples where such transformations apply?

**Tip**: Factoring out common terms is a key strategy in simplifying algebraic fractions, making it easier to work with them.

Discover how to simplify the algebraic fraction (3a+3b)/(2a-2b) using the given condition (a+b)/(a-b) = c. This step-by-step guide covers rational expressions, factoring, and substitution, suitable for students in Grades 9-12.

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