Basic Math Examples

$\frac{9}{y - 6} \cdot \frac{y + 5}{y^{2} - y - 30}$

Step 1

Factor $y^{2} - y - 30$ 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 $- 30$ and whose sum is $- 1$ .

$- 6, 5$

Step 1.2

Write the factored form using these integers.

$\frac{9}{y - 6} \cdot \frac{y + 5}{(y - 6) (y + 5)}$

Step 2

Cancel the common factor of $y + 5$ .

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Step 2.1

Cancel the common factor.

$\frac{9}{y - 6} \cdot \frac{y + 5}{(y - 6) (y + 5)}$

Step 2.2

Rewrite the expression.

$\frac{9}{y - 6} \cdot \frac{1}{y - 6}$

Step 3

Multiply $\frac{9}{y - 6} \cdot \frac{1}{y - 6}$ .

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Step 3.1

Multiply $\frac{9}{y - 6}$ by $\frac{1}{y - 6}$ .

$\frac{9}{(y - 6) (y - 6)}$

Step 3.2

Raise $y - 6$ to the power of $1$ .

$\frac{9}{{(y - 6)}^{1} (y - 6)}$

Step 3.3

Raise $y - 6$ to the power of $1$ .

$\frac{9}{{(y - 6)}^{1} {(y - 6)}^{1}}$

Step 3.4

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$\frac{9}{{(y - 6)}^{1 + 1}}$

Step 3.5

Add $1$ and $1$ .

$\frac{9}{{(y - 6)}^{2}}$