Algebra Examples

$\frac{2 x + 6}{x^{2} + 2 x - 24} \cdot \frac{x^{2} + 2 x - 24}{x^{2} - 7 x + 12}$

Step 1

Factor $2$ out of $2 x + 6$ .

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Step 1.1

Factor $2$ out of $2 x$ .

$\frac{2 (x) + 6}{x^{2} + 2 x - 24} \cdot \frac{x^{2} + 2 x - 24}{x^{2} - 7 x + 12}$

Step 1.2

Factor $2$ out of $6$ .

$\frac{2 x + 2 \cdot 3}{x^{2} + 2 x - 24} \cdot \frac{x^{2} + 2 x - 24}{x^{2} - 7 x + 12}$

Step 1.3

Factor $2$ out of $2 x + 2 \cdot 3$ .

$\frac{2 (x + 3)}{x^{2} + 2 x - 24} \cdot \frac{x^{2} + 2 x - 24}{x^{2} - 7 x + 12}$

Step 2

Factor $x^{2} + 2 x - 24$ 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 $- 24$ and whose sum is $2$ .

$- 4, 6$

Step 2.2

Write the factored form using these integers.

$\frac{2 (x + 3)}{(x - 4) (x + 6)} \cdot \frac{x^{2} + 2 x - 24}{x^{2} - 7 x + 12}$

Step 3

Factor $x^{2} + 2 x - 24$ 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 $- 24$ and whose sum is $2$ .

$- 4, 6$

Step 3.2

Write the factored form using these integers.

$\frac{2 (x + 3)}{(x - 4) (x + 6)} \cdot \frac{(x - 4) (x + 6)}{x^{2} - 7 x + 12}$

Step 4

Factor $x^{2} - 7 x + 12$ using the AC method.

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Step 4.1

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 $12$ and whose sum is $- 7$ .

$- 4, - 3$

Step 4.2

Write the factored form using these integers.

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

Step 5

Simplify terms.

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Step 5.1

Cancel the common factor of $(x - 4) (x + 6)$ .

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Step 5.1.1

Cancel the common factor.

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

Step 5.1.2

Rewrite the expression.

$2 (x + 3) \cdot \frac{1}{(x - 4) (x - 3)}$

Step 5.2

Combine $\frac{1}{(x - 4) (x - 3)}$ and $2$ .

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

Step 5.3

Multiply $\frac{2}{(x - 4) (x - 3)}$ by $x + 3$ .

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