Algebra Examples

$\frac{2 x + 16}{x^{2} + 3 x - 40} \cdot \frac{x^{2} - 11 x + 30}{x^{2} - 14 x + 48}$

Step 1

Factor $2$ out of $2 x + 16$ .

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Step 1.1

Factor $2$ out of $2 x$ .

$\frac{2 (x) + 16}{x^{2} + 3 x - 40} \cdot \frac{x^{2} - 11 x + 30}{x^{2} - 14 x + 48}$

Step 1.2

Factor $2$ out of $16$ .

$\frac{2 x + 2 \cdot 8}{x^{2} + 3 x - 40} \cdot \frac{x^{2} - 11 x + 30}{x^{2} - 14 x + 48}$

Step 1.3

Factor $2$ out of $2 x + 2 \cdot 8$ .

$\frac{2 (x + 8)}{x^{2} + 3 x - 40} \cdot \frac{x^{2} - 11 x + 30}{x^{2} - 14 x + 48}$

Step 2

Factor $x^{2} + 3 x - 40$ 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 $- 40$ and whose sum is $3$ .

$- 5, 8$

Step 2.2

Write the factored form using these integers.

$\frac{2 (x + 8)}{(x - 5) (x + 8)} \cdot \frac{x^{2} - 11 x + 30}{x^{2} - 14 x + 48}$

Step 3

Factor $x^{2} - 11 x + 30$ 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 $30$ and whose sum is $- 11$ .

$- 6, - 5$

Step 3.2

Write the factored form using these integers.

$\frac{2 (x + 8)}{(x - 5) (x + 8)} \cdot \frac{(x - 6) (x - 5)}{x^{2} - 14 x + 48}$

Step 4

Factor $x^{2} - 14 x + 48$ 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 $48$ and whose sum is $- 14$ .

$- 8, - 6$

Step 4.2

Write the factored form using these integers.

$\frac{2 (x + 8)}{(x - 5) (x + 8)} \cdot \frac{(x - 6) (x - 5)}{(x - 8) (x - 6)}$

Step 5

Simplify terms.

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Step 5.1

Cancel the common factor of $x - 5$ .

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Step 5.1.1

Factor $x - 5$ out of $(x - 6) (x - 5)$ .

$\frac{2 (x + 8)}{(x - 5) (x + 8)} \cdot \frac{(x - 5) (x - 6)}{(x - 8) (x - 6)}$

Step 5.1.2

Cancel the common factor.

$\frac{2 (x + 8)}{(x - 5) (x + 8)} \cdot \frac{(x - 5) (x - 6)}{(x - 8) (x - 6)}$

Step 5.1.3

Rewrite the expression.

$\frac{2 (x + 8)}{x + 8} \cdot \frac{x - 6}{(x - 8) (x - 6)}$

Step 5.2

Multiply $\frac{2 (x + 8)}{x + 8}$ by $\frac{x - 6}{(x - 8) (x - 6)}$ .

$\frac{2 (x + 8) (x - 6)}{(x + 8) ((x - 8) (x - 6))}$

Step 5.3

Cancel the common factor of $x + 8$ .

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Step 5.3.1

Cancel the common factor.

$\frac{2 (x + 8) (x - 6)}{(x + 8) ((x - 8) (x - 6))}$

Step 5.3.2

Rewrite the expression.

$\frac{2 (x - 6)}{(x - 8) (x - 6)}$

Step 5.4

Cancel the common factor of $x - 6$ .

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Step 5.4.1

Cancel the common factor.

$\frac{2 (x - 6)}{(x - 8) (x - 6)}$

Step 5.4.2

Rewrite the expression.

$\frac{2}{x - 8}$