Basic Math Examples

$\frac{d + 1}{3 d + 9} \cdot \frac{d^{2} + d - 6}{d^{2} + 3 d + 2}$

Step 1

Factor $3$ out of $3 d + 9$ .

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Step 1.1

Factor $3$ out of $3 d$ .

$\frac{d + 1}{3 (d) + 9} \cdot \frac{d^{2} + d - 6}{d^{2} + 3 d + 2}$

Step 1.2

Factor $3$ out of $9$ .

$\frac{d + 1}{3 d + 3 \cdot 3} \cdot \frac{d^{2} + d - 6}{d^{2} + 3 d + 2}$

Step 1.3

Factor $3$ out of $3 d + 3 \cdot 3$ .

$\frac{d + 1}{3 (d + 3)} \cdot \frac{d^{2} + d - 6}{d^{2} + 3 d + 2}$

Step 2

Factor $d^{2} + d - 6$ using the AC method.

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Step 2.1

Consider the form $x^{2} + b x + c$ . Find a pair of integers whose product is $c$ and whose sum is $b$ . In this case, whose product is $- 6$ and whose sum is $1$ .

$- 2, 3$

Step 2.2

Write the factored form using these integers.

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

Step 3

Factor $d^{2} + 3 d + 2$ using the AC method.

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Step 3.1

Consider the form $x^{2} + b x + c$ . Find a pair of integers whose product is $c$ and whose sum is $b$ . In this case, whose product is $2$ and whose sum is $3$ .

$1, 2$

Step 3.2

Write the factored form using these integers.

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

Step 4

Simplify terms.

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Step 4.1

Cancel the common factor of $d + 1$ .

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Step 4.1.1

Cancel the common factor.

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

Step 4.1.2

Rewrite the expression.

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

Step 4.2

Cancel the common factor of $d + 3$ .

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Step 4.2.1

Factor $d + 3$ out of $3 (d + 3)$ .

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

Step 4.2.2

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

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

Step 4.2.3

Cancel the common factor.

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

Step 4.2.4

Rewrite the expression.

$\frac{1}{3} \cdot \frac{d - 2}{d + 2}$

Step 4.3

Multiply $\frac{1}{3}$ by $\frac{d - 2}{d + 2}$ .

$\frac{d - 2}{3 (d + 2)}$