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The problem asks us to find the value of \( c \) given that:

\[
\frac{c - d}{c + d} = 2 \quad \text{and} \quad d = 1.
\]

Let's solve this step by step:

### Step 1: Substitute \( d = 1 \)
Substitute \( d = 1 \) into the equation:

\[
\frac{c - 1}{c + 1} = 2.
\]

### Step 2: Cross-multiply to solve for \( c \)
Cross-multiply to eliminate the fraction:

\[
c - 1 = 2(c + 1).
\]

### Step 3: Expand and simplify
Expand the right side:

\[
c - 1 = 2c + 2.
\]

Bring terms involving \( c \) to one side:

\[
-1 - 2 = c.
\]

\[
c = -3.
\]

### Final Answer:
The value of \( c \) is \(\boxed{-3}\).

Would you like a detailed explanation or have any questions?

### Related Questions:
1. How do you solve equations involving fractions like \(\frac{c - d}{c + d} = 2\)?
2. What is cross-multiplication, and when is it used?
3. How would the solution change if \( d \) had a different value?
4. How can you check your answer when solving equations?
5. What are common mistakes to avoid when solving rational equations?

### Tip:
When solving equations involving fractions, always consider cross-multiplying as a way to eliminate the fraction, making it easier to solve for the unknown variable.

If \( \frac{c - d}{c + d} = 2 \) and \( d = 1 \), what is the value of \( c \)?

Learn how to solve the algebraic equation \( \frac{c - d}{c + d} = 2 \) where \( d = 1 \). This problem involves key algebra concepts, including cross-multiplication and rational equations. Suitable for students in Grades 8-10.

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