Algebra Examples

$\frac{9 - d^{2}}{d + 3} \cdot \frac{d}{d - 3}$

Step 1

Simplify the numerator.

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Step 1.1

Rewrite $9$ as $3^{2}$ .

$\frac{3^{2} - d^{2}}{d + 3} \cdot \frac{d}{d - 3}$

Step 1.2

Since both terms are perfect squares, factor using the difference of squares formula, $a^{2} - b^{2} = (a + b) (a - b)$ where $a = 3$ and $b = d$ .

$\frac{(3 + d) (3 - d)}{d + 3} \cdot \frac{d}{d - 3}$

Step 2

Simplify terms.

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Step 2.1

Cancel the common factor of $3 + d$ and $d + 3$ .

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Step 2.1.1

Reorder terms.

$\frac{(d + 3) (3 - d)}{d + 3} \cdot \frac{d}{d - 3}$

Step 2.1.2

Cancel the common factor.

$\frac{(d + 3) (3 - d)}{d + 3} \cdot \frac{d}{d - 3}$

Step 2.1.3

Divide $3 - d$ by $1$ .

$(3 - d) \cdot \frac{d}{d - 3}$

Step 2.2

Multiply $3 - d$ by $\frac{d}{d - 3}$ .

$\frac{(3 - d) d}{d - 3}$

Step 2.3

Cancel the common factor of $3 - d$ and $d - 3$ .

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Step 2.3.1

Rewrite $3$ as $- 1 (- 3)$ .

$\frac{(- 1 (- 3) - d) d}{d - 3}$

Step 2.3.2

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

$\frac{(- 1 (- 3) - (d)) d}{d - 3}$

Step 2.3.3

Factor $- 1$ out of $- 1 (- 3) - (d)$ .

$\frac{- 1 (- 3 + d) d}{d - 3}$

Step 2.3.4

Reorder terms.

$\frac{- 1 (d - 3) d}{d - 3}$

Step 2.3.5

Cancel the common factor.

$\frac{- 1 (d - 3) d}{d - 3}$

Step 2.3.6

Divide $- 1 d$ by $1$ .

$- 1 d$

Step 2.4

Rewrite $- 1 d$ as $- d$ .

$- d$