Basic Math Examples

$\frac{3 u^{2} + 12 u - 96}{u^{2} + 12 u + 32 u}$

Step 1

Simplify the numerator.

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Step 1.1

Factor $3$ out of $3 u^{2} + 12 u - 96$ .

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Step 1.1.1

Factor $3$ out of $3 u^{2}$ .

$\frac{3 (u^{2}) + 12 u - 96}{u^{2} + 12 u + 32 u}$

Step 1.1.2

Factor $3$ out of $12 u$ .

$\frac{3 (u^{2}) + 3 (4 u) - 96}{u^{2} + 12 u + 32 u}$

Step 1.1.3

Factor $3$ out of $- 96$ .

$\frac{3 u^{2} + 3 (4 u) + 3 \cdot - 32}{u^{2} + 12 u + 32 u}$

Step 1.1.4

Factor $3$ out of $3 u^{2} + 3 (4 u)$ .

$\frac{3 (u^{2} + 4 u) + 3 \cdot - 32}{u^{2} + 12 u + 32 u}$

Step 1.1.5

Factor $3$ out of $3 (u^{2} + 4 u) + 3 \cdot - 32$ .

$\frac{3 (u^{2} + 4 u - 32)}{u^{2} + 12 u + 32 u}$

Step 1.2

Factor $u^{2} + 4 u - 32$ using the AC method.

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Step 1.2.1

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 $- 32$ and whose sum is $4$ .

$- 4, 8$

Step 1.2.2

Write the factored form using these integers.

$\frac{3 ((u - 4) (u + 8))}{u^{2} + 12 u + 32 u}$

$\frac{3 (u - 4) (u + 8)}{u^{2} + 12 u + 32 u}$

Step 2

Simplify the denominator.

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Step 2.1

Add $12 u$ and $32 u$ .

$\frac{3 (u - 4) (u + 8)}{u^{2} + 44 u}$

Step 2.2

Factor $u$ out of $u^{2} + 44 u$ .

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Step 2.2.1

Factor $u$ out of $u^{2}$ .

$\frac{3 (u - 4) (u + 8)}{u \cdot u + 44 u}$

Step 2.2.2

Factor $u$ out of $44 u$ .

$\frac{3 (u - 4) (u + 8)}{u \cdot u + u \cdot 44}$

Step 2.2.3

Factor $u$ out of $u \cdot u + u \cdot 44$ .

$\frac{3 (u - 4) (u + 8)}{u (u + 44)}$