Algebra Examples

$\frac{\frac{15 x - 10}{x - 8}}{\frac{3 x - 2}{x^{2} - 12 x + 32}}$

Step 1

Multiply the numerator by the reciprocal of the denominator.

$\frac{15 x - 10}{x - 8} \cdot \frac{x^{2} - 12 x + 32}{3 x - 2}$

Step 2

Factor $5$ out of $15 x - 10$ .

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Step 2.1

Factor $5$ out of $15 x$ .

$\frac{5 (3 x) - 10}{x - 8} \cdot \frac{x^{2} - 12 x + 32}{3 x - 2}$

Step 2.2

Factor $5$ out of $- 10$ .

$\frac{5 (3 x) + 5 (- 2)}{x - 8} \cdot \frac{x^{2} - 12 x + 32}{3 x - 2}$

Step 2.3

Factor $5$ out of $5 (3 x) + 5 (- 2)$ .

$\frac{5 (3 x - 2)}{x - 8} \cdot \frac{x^{2} - 12 x + 32}{3 x - 2}$

Step 3

Cancel the common factor of $3 x - 2$ .

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Step 3.1

Factor $3 x - 2$ out of $5 (3 x - 2)$ .

$\frac{(3 x - 2) \cdot 5}{x - 8} \cdot \frac{x^{2} - 12 x + 32}{3 x - 2}$

Step 3.2

Cancel the common factor.

$\frac{(3 x - 2) \cdot 5}{x - 8} \cdot \frac{x^{2} - 12 x + 32}{3 x - 2}$

Step 3.3

Rewrite the expression.

$\frac{5}{x - 8} (x^{2} - 12 x + 32)$

Step 4

Multiply $\frac{5}{x - 8}$ by $x^{2} - 12 x + 32$ .

$\frac{5 (x^{2} - 12 x + 32)}{x - 8}$

Step 5

Factor $x^{2} - 12 x + 32$ using the AC method.

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Step 5.1

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 $32$ and whose sum is $- 12$ .

$- 8, - 4$

Step 5.2

Write the factored form using these integers.

$\frac{5 ((x - 8) (x - 4))}{x - 8}$

$\frac{5 (x - 8) (x - 4)}{x - 8}$

Step 6

Cancel the common factor of $x - 8$ .

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Step 6.1

Cancel the common factor.

$\frac{5 (x - 8) (x - 4)}{x - 8}$

Step 6.2

Divide $5 (x - 4)$ by $1$ .

$5 (x - 4)$

Step 7

Apply the distributive property.

$5 x + 5 \cdot - 4$

Step 8

Multiply $5$ by $- 4$ .

$5 x - 20$