Basic Math Examples

$\frac{7}{v + 2} - \frac{3}{v - 2}$

Step 1

To write $\frac{7}{v + 2}$ as a fraction with a common denominator, multiply by $\frac{v - 2}{v - 2}$ .

$\frac{7}{v + 2} \cdot \frac{v - 2}{v - 2} - \frac{3}{v - 2}$

Step 2

To write $- \frac{3}{v - 2}$ as a fraction with a common denominator, multiply by $\frac{v + 2}{v + 2}$ .

$\frac{7}{v + 2} \cdot \frac{v - 2}{v - 2} - \frac{3}{v - 2} \cdot \frac{v + 2}{v + 2}$

Step 3

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

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Step 3.1

Multiply $\frac{7}{v + 2}$ by $\frac{v - 2}{v - 2}$ .

$\frac{7 (v - 2)}{(v + 2) (v - 2)} - \frac{3}{v - 2} \cdot \frac{v + 2}{v + 2}$

Step 3.2

Multiply $\frac{3}{v - 2}$ by $\frac{v + 2}{v + 2}$ .

$\frac{7 (v - 2)}{(v + 2) (v - 2)} - \frac{3 (v + 2)}{(v - 2) (v + 2)}$

Step 3.3

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

$\frac{7 (v - 2)}{(v + 2) (v - 2)} - \frac{3 (v + 2)}{(v + 2) (v - 2)}$

Step 4

Combine the numerators over the common denominator.

$\frac{7 (v - 2) - 3 (v + 2)}{(v + 2) (v - 2)}$

Step 5

Simplify the numerator.

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Step 5.1

Apply the distributive property.

$\frac{7 v + 7 \cdot - 2 - 3 (v + 2)}{(v + 2) (v - 2)}$

Step 5.2

Multiply $7$ by $- 2$ .

$\frac{7 v - 14 - 3 (v + 2)}{(v + 2) (v - 2)}$

Step 5.3

Apply the distributive property.

$\frac{7 v - 14 - 3 v - 3 \cdot 2}{(v + 2) (v - 2)}$

Step 5.4

Multiply $- 3$ by $2$ .

$\frac{7 v - 14 - 3 v - 6}{(v + 2) (v - 2)}$

Step 5.5

Subtract $3 v$ from $7 v$ .

$\frac{4 v - 14 - 6}{(v + 2) (v - 2)}$

Step 5.6

Subtract $6$ from $- 14$ .

$\frac{4 v - 20}{(v + 2) (v - 2)}$

Step 5.7

Factor $4$ out of $4 v - 20$ .

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Step 5.7.1

Factor $4$ out of $4 v$ .

$\frac{4 (v) - 20}{(v + 2) (v - 2)}$

Step 5.7.2

Factor $4$ out of $- 20$ .

$\frac{4 v + 4 \cdot - 5}{(v + 2) (v - 2)}$

Step 5.7.3

Factor $4$ out of $4 v + 4 \cdot - 5$ .

$\frac{4 (v - 5)}{(v + 2) (v - 2)}$