Basic Math Examples

$\frac{c - d}{c + 2 d} \cdot \frac{2 d + c}{d + c} \div \frac{d - c}{d + c}$

Step 1

To divide by a fraction, multiply by its reciprocal.

$\frac{c - d}{c + 2 d} \cdot \frac{2 d + c}{d + c} \frac{d + c}{d - c}$

Step 2

Multiply $\frac{c - d}{c + 2 d}$ by $\frac{2 d + c}{d + c}$ .

$\frac{(c - d) (2 d + c)}{(c + 2 d) (d + c)} \cdot \frac{d + c}{d - c}$

Step 3

Cancel the common factor of $d + c$ .

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Step 3.1

Factor $d + c$ out of $(c + 2 d) (d + c)$ .

$\frac{(c - d) (2 d + c)}{(d + c) (c + 2 d)} \cdot \frac{d + c}{d - c}$

Step 3.2

Cancel the common factor.

$\frac{(c - d) (2 d + c)}{(d + c) (c + 2 d)} \cdot \frac{d + c}{d - c}$

Step 3.3

Rewrite the expression.

$\frac{(c - d) (2 d + c)}{c + 2 d} \cdot \frac{1}{d - c}$

Step 4

Multiply $\frac{(c - d) (2 d + c)}{c + 2 d}$ by $\frac{1}{d - c}$ .

$\frac{(c - d) (2 d + c)}{(c + 2 d) (d - c)}$

Step 5

Cancel the common factor of $c - d$ and $d - c$ .

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Step 5.1

Factor $- 1$ out of $c$ .

$\frac{(- 1 (- c) - d) (2 d + c)}{(c + 2 d) (d - c)}$

Step 5.2

Factor $- 1$ out of $- d$ .

$\frac{(- 1 (- c) - (d)) (2 d + c)}{(c + 2 d) (d - c)}$

Step 5.3

Factor $- 1$ out of $- 1 (- c) - (d)$ .

$\frac{- 1 (- c + d) (2 d + c)}{(c + 2 d) (d - c)}$

Step 5.4

Reorder terms.

$\frac{- 1 (- c + d) (2 d + c)}{(c + 2 d) (- c + d)}$

Step 5.5

Cancel the common factor.

$\frac{- 1 (- c + d) (2 d + c)}{(c + 2 d) (- c + d)}$

Step 5.6

Rewrite the expression.

$\frac{- 1 (2 d + c)}{c + 2 d}$

Step 6

Cancel the common factor of $2 d + c$ and $c + 2 d$ .

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Step 6.1

Reorder terms.

$\frac{- 1 (c + 2 d)}{c + 2 d}$

Step 6.2

Cancel the common factor.

$\frac{- 1 (c + 2 d)}{c + 2 d}$

Step 6.3

Divide $- 1$ by $1$ .

$- 1$