Basic Math Examples

$\frac{a + 2}{a - 5} \div \frac{a + 1}{a^{2} - 8 a + 15}$

Step 1

To divide by a fraction, multiply by its reciprocal.

$\frac{a + 2}{a - 5} \cdot \frac{a^{2} - 8 a + 15}{a + 1}$

Step 2

Factor $a^{2} - 8 a + 15$ 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 $15$ and whose sum is $- 8$ .

$- 5, - 3$

Step 2.2

Write the factored form using these integers.

$\frac{a + 2}{a - 5} \cdot \frac{(a - 5) (a - 3)}{a + 1}$

Step 3

Simplify terms.

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Step 3.1

Cancel the common factor of $a - 5$ .

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Step 3.1.1

Cancel the common factor.

$\frac{a + 2}{a - 5} \cdot \frac{(a - 5) (a - 3)}{a + 1}$

Step 3.1.2

Rewrite the expression.

$(a + 2) \frac{a - 3}{a + 1}$

Step 3.2

Multiply $a + 2$ by $\frac{a - 3}{a + 1}$ .

$\frac{(a + 2) (a - 3)}{a + 1}$