Basic Math Examples

$(\frac{c - 2}{c + 2} - \frac{c}{c - 2}) \cdot \frac{c + 2}{2 - 3 \cdot c}$

Step 1

To write $\frac{c - 2}{c + 2}$ as a fraction with a common denominator, multiply by $\frac{c - 2}{c - 2}$ .

$(\frac{c - 2}{c + 2} \cdot \frac{c - 2}{c - 2} - \frac{c}{c - 2}) \cdot \frac{c + 2}{2 - 3 \cdot c}$

Step 2

To write $- \frac{c}{c - 2}$ as a fraction with a common denominator, multiply by $\frac{c + 2}{c + 2}$ .

$(\frac{c - 2}{c + 2} \cdot \frac{c - 2}{c - 2} - \frac{c}{c - 2} \cdot \frac{c + 2}{c + 2}) \cdot \frac{c + 2}{2 - 3 \cdot c}$

Step 3

Write each expression with a common denominator of $(c + 2) (c - 2)$ , by multiplying each by an appropriate factor of $1$ .

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Step 3.1

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

$(\frac{(c - 2) (c - 2)}{(c + 2) (c - 2)} - \frac{c}{c - 2} \cdot \frac{c + 2}{c + 2}) \cdot \frac{c + 2}{2 - 3 \cdot c}$

Step 3.2

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

$(\frac{(c - 2) (c - 2)}{(c + 2) (c - 2)} - \frac{c (c + 2)}{(c - 2) (c + 2)}) \cdot \frac{c + 2}{2 - 3 \cdot c}$

Step 3.3

Reorder the factors of $(c - 2) (c + 2)$ .

$(\frac{(c - 2) (c - 2)}{(c + 2) (c - 2)} - \frac{c (c + 2)}{(c + 2) (c - 2)}) \cdot \frac{c + 2}{2 - 3 \cdot c}$

Step 4

Combine the numerators over the common denominator.

$\frac{(c - 2) (c - 2) - c (c + 2)}{(c + 2) (c - 2)} \cdot \frac{c + 2}{2 - 3 \cdot c}$

Step 5

Simplify the numerator.

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Step 5.1

Expand $(c - 2) (c - 2)$ using the FOIL Method.

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Step 5.1.1

Apply the distributive property.

$\frac{c (c - 2) - 2 (c - 2) - c (c + 2)}{(c + 2) (c - 2)} \cdot \frac{c + 2}{2 - 3 \cdot c}$

Step 5.1.2

Apply the distributive property.

$\frac{c \cdot c + c \cdot - 2 - 2 (c - 2) - c (c + 2)}{(c + 2) (c - 2)} \cdot \frac{c + 2}{2 - 3 \cdot c}$

Step 5.1.3

Apply the distributive property.

$\frac{c \cdot c + c \cdot - 2 - 2 c - 2 \cdot - 2 - c (c + 2)}{(c + 2) (c - 2)} \cdot \frac{c + 2}{2 - 3 \cdot c}$

Step 5.2

Simplify and combine like terms.

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Step 5.2.1

Simplify each term.

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Step 5.2.1.1

Multiply $c$ by $c$ .

$\frac{c^{2} + c \cdot - 2 - 2 c - 2 \cdot - 2 - c (c + 2)}{(c + 2) (c - 2)} \cdot \frac{c + 2}{2 - 3 \cdot c}$

Step 5.2.1.2

Move $- 2$ to the left of $c$ .

$\frac{c^{2} - 2 \cdot c - 2 c - 2 \cdot - 2 - c (c + 2)}{(c + 2) (c - 2)} \cdot \frac{c + 2}{2 - 3 \cdot c}$

Step 5.2.1.3

Multiply $- 2$ by $- 2$ .

$\frac{c^{2} - 2 c - 2 c + 4 - c (c + 2)}{(c + 2) (c - 2)} \cdot \frac{c + 2}{2 - 3 \cdot c}$

Step 5.2.2

Subtract $2 c$ from $- 2 c$ .

$\frac{c^{2} - 4 c + 4 - c (c + 2)}{(c + 2) (c - 2)} \cdot \frac{c + 2}{2 - 3 \cdot c}$

Step 5.3

Apply the distributive property.

$\frac{c^{2} - 4 c + 4 - c \cdot c - c \cdot 2}{(c + 2) (c - 2)} \cdot \frac{c + 2}{2 - 3 \cdot c}$

Step 5.4

Multiply $c$ by $c$ by adding the exponents.

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Step 5.4.1

Move $c$ .

$\frac{c^{2} - 4 c + 4 - (c \cdot c) - c \cdot 2}{(c + 2) (c - 2)} \cdot \frac{c + 2}{2 - 3 \cdot c}$

Step 5.4.2

Multiply $c$ by $c$ .

$\frac{c^{2} - 4 c + 4 - c^{2} - c \cdot 2}{(c + 2) (c - 2)} \cdot \frac{c + 2}{2 - 3 \cdot c}$

Step 5.5

Multiply $2$ by $- 1$ .

$\frac{c^{2} - 4 c + 4 - c^{2} - 2 c}{(c + 2) (c - 2)} \cdot \frac{c + 2}{2 - 3 \cdot c}$

Step 5.6

Subtract $c^{2}$ from $c^{2}$ .

$\frac{- 4 c + 4 + 0 - 2 c}{(c + 2) (c - 2)} \cdot \frac{c + 2}{2 - 3 \cdot c}$

Step 5.7

Add $- 4 c$ and $0$ .

$\frac{- 4 c + 4 - 2 c}{(c + 2) (c - 2)} \cdot \frac{c + 2}{2 - 3 \cdot c}$

Step 5.8

Subtract $2 c$ from $- 4 c$ .

$\frac{- 6 c + 4}{(c + 2) (c - 2)} \cdot \frac{c + 2}{2 - 3 \cdot c}$

Step 5.9

Factor $2$ out of $- 6 c + 4$ .

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Step 5.9.1

Factor $2$ out of $- 6 c$ .

$\frac{2 (- 3 c) + 4}{(c + 2) (c - 2)} \cdot \frac{c + 2}{2 - 3 \cdot c}$

Step 5.9.2

Factor $2$ out of $4$ .

$\frac{2 (- 3 c) + 2 (2)}{(c + 2) (c - 2)} \cdot \frac{c + 2}{2 - 3 \cdot c}$

Step 5.9.3

Factor $2$ out of $2 (- 3 c) + 2 (2)$ .

$\frac{2 (- 3 c + 2)}{(c + 2) (c - 2)} \cdot \frac{c + 2}{2 - 3 \cdot c}$

Step 6

Simplify terms.

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Step 6.1

Cancel the common factor of $c + 2$ .

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Step 6.1.1

Cancel the common factor.

$\frac{2 (- 3 c + 2)}{(c + 2) (c - 2)} \cdot \frac{c + 2}{2 - 3 \cdot c}$

Step 6.1.2

Rewrite the expression.

$\frac{2 (- 3 c + 2)}{c - 2} \cdot \frac{1}{2 - 3 \cdot c}$

Step 6.2

Multiply $\frac{2 (- 3 c + 2)}{c - 2}$ by $\frac{1}{2 - 3 \cdot c}$ .

$\frac{2 (- 3 c + 2)}{(c - 2) (2 - 3 \cdot c)}$

Step 6.3

Cancel the common factor of $- 3 c + 2$ and $2 - 3 \cdot c$ .

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Step 6.3.1

Reorder terms.

$\frac{2 (- 3 c + 2)}{(c - 2) (- 3 \cdot c + 2)}$

Step 6.3.2

Cancel the common factor.

$\frac{2 (- 3 c + 2)}{(c - 2) (- 3 \cdot c + 2)}$

Step 6.3.3

Rewrite the expression.

$\frac{2}{c - 2}$