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.