Basic Math Examples

$\frac{\frac{1}{5} \cdot (1 c + 1)}{\frac{1}{10} \cdot (c^{2} - 2 c - 3)}$

Step 1

Multiply $c$ by $1$ .

$\frac{\frac{1}{5} (c + 1)}{\frac{1}{10} \cdot (c^{2} - 2 c - 3)}$

Step 2

Factor $c^{2} - 2 c - 3$ 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 $- 3$ and whose sum is $- 2$ .

$- 3, 1$

Step 2.2

Write the factored form using these integers.

$\frac{\frac{1}{5} (c + 1)}{\frac{1}{10} ((c - 3) (c + 1))}$

$\frac{\frac{1}{5} (c + 1)}{\frac{1}{10} (c - 3) (c + 1)}$

Step 3

Cancel the common factor of $c + 1$ .

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Step 3.1

Cancel the common factor.

$\frac{\frac{1}{5} (c + 1)}{\frac{1}{10} (c - 3) (c + 1)}$

Step 3.2

Rewrite the expression.

$\frac{\frac{1}{5}}{\frac{1}{10} (c - 3)}$

Step 4

Multiply the numerator by the reciprocal of the denominator.

$\frac{1}{5} \cdot \frac{1}{\frac{1}{10} (c - 3)}$

Step 5

Factor $\frac{1}{10}$ out of $\frac{1}{\frac{1}{10} (c - 3)}$ .

$\frac{1}{5} (10 \frac{1}{c - 3})$

Step 6

Cancel the common factor of $5$ .

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Step 6.1

Factor $5$ out of $10 \frac{1}{c - 3}$ .

$\frac{1}{5} (5 (2 \frac{1}{c - 3}))$

Step 6.2

Cancel the common factor.

$\frac{1}{5} (5 (2 \frac{1}{c - 3}))$

Step 6.3

Rewrite the expression.

$2 \frac{1}{c - 3}$

Step 7

Combine $2$ and $\frac{1}{c - 3}$ .

$\frac{2}{c - 3}$