Basic Math Examples

$\frac{a^{2} - 6 a}{- 4} \div \frac{a - 6}{a}$

Step 1

To divide by a fraction, multiply by its reciprocal.

$\frac{a^{2} - 6 a}{- 4} \cdot \frac{a}{a - 6}$

Step 2

Factor $a$ out of $a^{2} - 6 a$ .

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Step 2.1

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

$\frac{a \cdot a - 6 a}{- 4} \cdot \frac{a}{a - 6}$

Step 2.2

Factor $a$ out of $- 6 a$ .

$\frac{a \cdot a + a \cdot - 6}{- 4} \cdot \frac{a}{a - 6}$

Step 2.3

Factor $a$ out of $a \cdot a + a \cdot - 6$ .

$\frac{a (a - 6)}{- 4} \cdot \frac{a}{a - 6}$

Step 3

Cancel the common factor of $a - 6$ .

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Step 3.1

Factor $a - 6$ out of $a (a - 6)$ .

$\frac{(a - 6) a}{- 4} \cdot \frac{a}{a - 6}$

Step 3.2

Cancel the common factor.

$\frac{(a - 6) a}{- 4} \cdot \frac{a}{a - 6}$

Step 3.3

Rewrite the expression.

$\frac{a}{- 4} a$

Step 4

Combine $\frac{a}{- 4}$ and $a$ .

$\frac{a \cdot a}{- 4}$

Step 5

Raise $a$ to the power of $1$ .

$\frac{a^{1} a}{- 4}$

Step 6

Raise $a$ to the power of $1$ .

$\frac{a^{1} a^{1}}{- 4}$

Step 7

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

$\frac{a^{1 + 1}}{- 4}$

Step 8

Add $1$ and $1$ .

$\frac{a^{2}}{- 4}$

Step 9

Move the negative in front of the fraction.

$- \frac{a^{2}}{4}$