Basic Math Examples

$\frac{u^{2} + u - 20}{3 u - 12}$

Step 1

Factor $u^{2} + u - 20$ using the AC method.

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Step 1.1

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 $1$ .

$- 4, 5$

Step 1.2

Write the factored form using these integers.

$\frac{(u - 4) (u + 5)}{3 u - 12}$

Step 2

Simplify terms.

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Step 2.1

Factor $3$ out of $3 u - 12$ .

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Step 2.1.1

Factor $3$ out of $3 u$ .

$\frac{(u - 4) (u + 5)}{3 (u) - 12}$

Step 2.1.2

Factor $3$ out of $- 12$ .

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

Step 2.1.3

Factor $3$ out of $3 u + 3 \cdot - 4$ .

$\frac{(u - 4) (u + 5)}{3 (u - 4)}$

Step 2.2

Cancel the common factor of $u - 4$ .

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Step 2.2.1

Cancel the common factor.

$\frac{(u - 4) (u + 5)}{3 (u - 4)}$

Step 2.2.2

Rewrite the expression.

$\frac{u + 5}{3}$