Basic Math Examples

$g (5) = \frac{x^{2} + x - 12}{x^{2} - 4 x - 12}$

Step 1

Divide each term in $g (5) = \frac{x^{2} + x - 12}{x^{2} - 4 x - 12}$ by $5$ .

$\frac{g \cdot 5}{5} = \frac{\frac{x^{2} + x - 12}{x^{2} - 4 x - 12}}{5}$

Step 2

Simplify the left side.

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Step 2.1

Cancel the common factor of $5$ .

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Step 2.1.1

Cancel the common factor.

$\frac{g \cdot 5}{5} = \frac{\frac{x^{2} + x - 12}{x^{2} - 4 x - 12}}{5}$

Step 2.1.2

Divide $g$ by $1$ .

$g = \frac{\frac{x^{2} + x - 12}{x^{2} - 4 x - 12}}{5}$

Step 3

Simplify the right side.

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Step 3.1

Multiply the numerator by the reciprocal of the denominator.

$g = \frac{x^{2} + x - 12}{x^{2} - 4 x - 12} \cdot \frac{1}{5}$

Step 3.2

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

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Step 3.2.1

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 $1$ .

$- 3, 4$

Step 3.2.2

Write the factored form using these integers.

$g = \frac{(x - 3) (x + 4)}{x^{2} - 4 x - 12} \cdot \frac{1}{5}$

Step 3.3

Factor $x^{2} - 4 x - 12$ using the AC method.

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Step 3.3.1

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 $- 12$ and whose sum is $- 4$ .

$- 6, 2$

Step 3.3.2

Write the factored form using these integers.

$g = \frac{(x - 3) (x + 4)}{(x - 6) (x + 2)} \cdot \frac{1}{5}$

Step 3.4

Combine fractions.

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Step 3.4.1

Multiply $\frac{(x - 3) (x + 4)}{(x - 6) (x + 2)}$ by $\frac{1}{5}$ .

$g = \frac{(x - 3) (x + 4)}{(x - 6) (x + 2) \cdot 5}$

Step 3.4.2

Move $5$ to the left of $(x - 6) (x + 2)$ .

$g = \frac{(x - 3) (x + 4)}{5 (x - 6) (x + 2)}$