Basic Math Examples

$\frac{2 u^{2} - 16 u + 24}{u^{2} - 7 u + 6}$

Step 1

Simplify the numerator.

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Step 1.1

Factor $2$ out of $2 u^{2} - 16 u + 24$ .

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Step 1.1.1

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

$\frac{2 (u^{2}) - 16 u + 24}{u^{2} - 7 u + 6}$

Step 1.1.2

Factor $2$ out of $- 16 u$ .

$\frac{2 (u^{2}) + 2 (- 8 u) + 24}{u^{2} - 7 u + 6}$

Step 1.1.3

Factor $2$ out of $24$ .

$\frac{2 u^{2} + 2 (- 8 u) + 2 \cdot 12}{u^{2} - 7 u + 6}$

Step 1.1.4

Factor $2$ out of $2 u^{2} + 2 (- 8 u)$ .

$\frac{2 (u^{2} - 8 u) + 2 \cdot 12}{u^{2} - 7 u + 6}$

Step 1.1.5

Factor $2$ out of $2 (u^{2} - 8 u) + 2 \cdot 12$ .

$\frac{2 (u^{2} - 8 u + 12)}{u^{2} - 7 u + 6}$

Step 1.2

Factor $u^{2} - 8 u + 12$ 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 $12$ and whose sum is $- 8$ .

$- 6, - 2$

Step 1.2.2

Write the factored form using these integers.

$\frac{2 ((u - 6) (u - 2))}{u^{2} - 7 u + 6}$

$\frac{2 (u - 6) (u - 2)}{u^{2} - 7 u + 6}$

Step 2

Factor $u^{2} - 7 u + 6$ 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 $6$ and whose sum is $- 7$ .

$- 6, - 1$

Step 2.2

Write the factored form using these integers.

$\frac{2 (u - 6) (u - 2)}{(u - 6) (u - 1)}$

Step 3

Cancel the common factor of $u - 6$ .

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Step 3.1

Cancel the common factor.

$\frac{2 (u - 6) (u - 2)}{(u - 6) (u - 1)}$

Step 3.2

Rewrite the expression.

$\frac{2 (u - 2)}{u - 1}$