Basic Math Examples

$\frac{n^{2} - 14 n + 40}{14} \cdot \frac{9}{9 n - 90}$

Step 1

Factor $n^{2} - 14 n + 40$ 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 $40$ and whose sum is $- 14$ .

$- 10, - 4$

Step 1.2

Write the factored form using these integers.

$\frac{(n - 10) (n - 4)}{14} \cdot \frac{9}{9 n - 90}$

Step 2

Simplify terms.

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Step 2.1

Factor $9$ out of $9 n - 90$ .

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Step 2.1.1

Factor $9$ out of $9 n$ .

$\frac{(n - 10) (n - 4)}{14} \cdot \frac{9}{9 (n) - 90}$

Step 2.1.2

Factor $9$ out of $- 90$ .

$\frac{(n - 10) (n - 4)}{14} \cdot \frac{9}{9 n + 9 \cdot - 10}$

Step 2.1.3

Factor $9$ out of $9 n + 9 \cdot - 10$ .

$\frac{(n - 10) (n - 4)}{14} \cdot \frac{9}{9 (n - 10)}$

Step 2.2

Cancel the common factor of $n - 10$ .

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Step 2.2.1

Factor $n - 10$ out of $9 (n - 10)$ .

$\frac{(n - 10) (n - 4)}{14} \cdot \frac{9}{(n - 10) \cdot 9}$

Step 2.2.2

Cancel the common factor.

$\frac{(n - 10) (n - 4)}{14} \cdot \frac{9}{(n - 10) \cdot 9}$

Step 2.2.3

Rewrite the expression.

$\frac{n - 4}{14} \cdot \frac{9}{9}$

Step 2.3

Multiply $\frac{n - 4}{14}$ by $\frac{9}{9}$ .

$\frac{(n - 4) \cdot 9}{14 \cdot 9}$

Step 2.4

Multiply $14$ by $9$ .

$\frac{(n - 4) \cdot 9}{126}$

Step 2.5

Cancel the common factor of $9$ and $126$ .

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Step 2.5.1

Factor $9$ out of $(n - 4) \cdot 9$ .

$\frac{9 \cdot (n - 4)}{126}$

Step 2.5.2

Cancel the common factors.

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Step 2.5.2.1

Factor $9$ out of $126$ .

$\frac{9 \cdot (n - 4)}{9 \cdot 14}$

Step 2.5.2.2

Cancel the common factor.

$\frac{9 \cdot (n - 4)}{9 \cdot 14}$

Step 2.5.2.3

Rewrite the expression.

$\frac{n - 4}{14}$