Algebra Examples

$\frac{4 x - 8}{x^{2} + 4 x - 12}$

Step 1

Factor $4$ out of $4 x - 8$ .

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Step 1.1

Factor $4$ out of $4 x$ .

$\frac{4 (x) - 8}{x^{2} + 4 x - 12}$

Step 1.2

Factor $4$ out of $- 8$ .

$\frac{4 x + 4 \cdot - 2}{x^{2} + 4 x - 12}$

Step 1.3

Factor $4$ out of $4 x + 4 \cdot - 2$ .

$\frac{4 (x - 2)}{x^{2} + 4 x - 12}$

Step 2

Factor $x^{2} + 4 x - 12$ 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 $- 12$ and whose sum is $4$ .

$- 2, 6$

Step 2.2

Write the factored form using these integers.

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

Step 3

Cancel the common factor of $x - 2$ .

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Step 3.1

Cancel the common factor.

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

Step 3.2

Rewrite the expression.

$\frac{4}{x + 6}$

Step 4

Finding the LCD of a list of values is the same as finding the LCM of the denominators of those values.

$x + 6$

Step 5

Remove parentheses.

$x + 6$