Algebra Examples

$\frac{8 x + 40}{x + 7} \cdot \frac{3}{2 x^{2} - 50}$

Step 1

Factor $8$ out of $8 x + 40$ .

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Step 1.1

Factor $8$ out of $8 x$ .

$\frac{8 (x) + 40}{x + 7} \cdot \frac{3}{2 x^{2} - 50}$

Step 1.2

Factor $8$ out of $40$ .

$\frac{8 x + 8 \cdot 5}{x + 7} \cdot \frac{3}{2 x^{2} - 50}$

Step 1.3

Factor $8$ out of $8 x + 8 \cdot 5$ .

$\frac{8 (x + 5)}{x + 7} \cdot \frac{3}{2 x^{2} - 50}$

Step 2

Simplify the denominator.

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Step 2.1

Factor $2$ out of $2 x^{2} - 50$ .

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Step 2.1.1

Factor $2$ out of $2 x^{2}$ .

$\frac{8 (x + 5)}{x + 7} \cdot \frac{3}{2 (x^{2}) - 50}$

Step 2.1.2

Factor $2$ out of $- 50$ .

$\frac{8 (x + 5)}{x + 7} \cdot \frac{3}{2 x^{2} + 2 \cdot - 25}$

Step 2.1.3

Factor $2$ out of $2 x^{2} + 2 \cdot - 25$ .

$\frac{8 (x + 5)}{x + 7} \cdot \frac{3}{2 (x^{2} - 25)}$

Step 2.2

Rewrite $25$ as $5^{2}$ .

$\frac{8 (x + 5)}{x + 7} \cdot \frac{3}{2 (x^{2} - 5^{2})}$

Step 2.3

Since both terms are perfect squares, factor using the difference of squares formula, $a^{2} - b^{2} = (a + b) (a - b)$ where $a = x$ and $b = 5$ .

$\frac{8 (x + 5)}{x + 7} \cdot \frac{3}{2 (x + 5) (x - 5)}$

Step 3

Simplify terms.

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Step 3.1

Cancel the common factor of $2 (x + 5)$ .

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Step 3.1.1

Factor $2 (x + 5)$ out of $8 (x + 5)$ .

$\frac{2 (x + 5) (4)}{x + 7} \cdot \frac{3}{2 (x + 5) (x - 5)}$

Step 3.1.2

Cancel the common factor.

$\frac{2 (x + 5) \cdot 4}{x + 7} \cdot \frac{3}{2 (x + 5) (x - 5)}$

Step 3.1.3

Rewrite the expression.

$\frac{4}{x + 7} \cdot \frac{3}{x - 5}$

Step 3.2

Multiply $\frac{4}{x + 7}$ by $\frac{3}{x - 5}$ .

$\frac{4 \cdot 3}{(x + 7) (x - 5)}$

Step 3.3

Multiply $4$ by $3$ .

$\frac{12}{(x + 7) (x - 5)}$