Basic Math Examples

$\frac{7}{w + 9} - \frac{2}{w - 9}$

Step 1

To write $\frac{7}{w + 9}$ as a fraction with a common denominator, multiply by $\frac{w - 9}{w - 9}$ .

$\frac{7}{w + 9} \cdot \frac{w - 9}{w - 9} - \frac{2}{w - 9}$

Step 2

To write $- \frac{2}{w - 9}$ as a fraction with a common denominator, multiply by $\frac{w + 9}{w + 9}$ .

$\frac{7}{w + 9} \cdot \frac{w - 9}{w - 9} - \frac{2}{w - 9} \cdot \frac{w + 9}{w + 9}$

Step 3

Write each expression with a common denominator of $(w + 9) (w - 9)$ , by multiplying each by an appropriate factor of $1$ .

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Step 3.1

Multiply $\frac{7}{w + 9}$ by $\frac{w - 9}{w - 9}$ .

$\frac{7 (w - 9)}{(w + 9) (w - 9)} - \frac{2}{w - 9} \cdot \frac{w + 9}{w + 9}$

Step 3.2

Multiply $\frac{2}{w - 9}$ by $\frac{w + 9}{w + 9}$ .

$\frac{7 (w - 9)}{(w + 9) (w - 9)} - \frac{2 (w + 9)}{(w - 9) (w + 9)}$

Step 3.3

Reorder the factors of $(w - 9) (w + 9)$ .

$\frac{7 (w - 9)}{(w + 9) (w - 9)} - \frac{2 (w + 9)}{(w + 9) (w - 9)}$

Step 4

Combine the numerators over the common denominator.

$\frac{7 (w - 9) - 2 (w + 9)}{(w + 9) (w - 9)}$

Step 5

Simplify the numerator.

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Step 5.1

Apply the distributive property.

$\frac{7 w + 7 \cdot - 9 - 2 (w + 9)}{(w + 9) (w - 9)}$

Step 5.2

Multiply $7$ by $- 9$ .

$\frac{7 w - 63 - 2 (w + 9)}{(w + 9) (w - 9)}$

Step 5.3

Apply the distributive property.

$\frac{7 w - 63 - 2 w - 2 \cdot 9}{(w + 9) (w - 9)}$

Step 5.4

Multiply $- 2$ by $9$ .

$\frac{7 w - 63 - 2 w - 18}{(w + 9) (w - 9)}$

Step 5.5

Subtract $2 w$ from $7 w$ .

$\frac{5 w - 63 - 18}{(w + 9) (w - 9)}$

Step 5.6

Subtract $18$ from $- 63$ .

$\frac{5 w - 81}{(w + 9) (w - 9)}$