Pre-Algebra Examples

$\frac{\frac{x^{2} + 6 x + 8}{x - 6}}{\frac{x^{2} - x - 20}{x - 6}}$

Step 1

Multiply the numerator by the reciprocal of the denominator.

$\frac{x^{2} + 6 x + 8}{x - 6} \cdot \frac{x - 6}{x^{2} - x - 20}$

Step 2

Cancel the common factor of $x - 6$ .

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Step 2.1

Cancel the common factor.

$\frac{x^{2} + 6 x + 8}{x - 6} \cdot \frac{x - 6}{x^{2} - x - 20}$

Step 2.2

Rewrite the expression.

$(x^{2} + 6 x + 8) \frac{1}{x^{2} - x - 20}$

Step 3

Factor $x^{2} - x - 20$ 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 $- 20$ and whose sum is $- 1$ .

$- 5, 4$

Step 3.2

Write the factored form using these integers.

$(x^{2} + 6 x + 8) \frac{1}{(x - 5) (x + 4)}$

Step 4

Multiply $x^{2} + 6 x + 8$ by $\frac{1}{(x - 5) (x + 4)}$ .

$\frac{x^{2} + 6 x + 8}{(x - 5) (x + 4)}$

Step 5

Factor $x^{2} + 6 x + 8$ 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 $8$ and whose sum is $6$ .

$2, 4$

Step 5.2

Write the factored form using these integers.

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

Step 6

Cancel the common factor of $x + 4$ .

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Step 6.1

Cancel the common factor.

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

Step 6.2

Rewrite the expression.

$\frac{x + 2}{x - 5}$