Basic Math Examples

$(3 a - 18) \div (a^{3} - 6 a^{2} + 3 a - 18)$

Step 1

Rewrite the division as a fraction.

$\frac{3 a - 18}{a^{3} - 6 a^{2} + 3 a - 18}$

Step 2

Factor $3$ out of $3 a - 18$ .

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Step 2.1

Factor $3$ out of $3 a$ .

$\frac{3 (a) - 18}{a^{3} - 6 a^{2} + 3 a - 18}$

Step 2.2

Factor $3$ out of $- 18$ .

$\frac{3 a + 3 \cdot - 6}{a^{3} - 6 a^{2} + 3 a - 18}$

Step 2.3

Factor $3$ out of $3 a + 3 \cdot - 6$ .

$\frac{3 (a - 6)}{a^{3} - 6 a^{2} + 3 a - 18}$

Step 3

Simplify the denominator.

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Step 3.1

Factor out the greatest common factor from each group.

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Step 3.1.1

Group the first two terms and the last two terms.

$\frac{3 (a - 6)}{(a^{3} - 6 a^{2}) + 3 a - 18}$

Step 3.1.2

Factor out the greatest common factor (GCF) from each group.

$\frac{3 (a - 6)}{a^{2} (a - 6) + 3 (a - 6)}$

Step 3.2

Factor the polynomial by factoring out the greatest common factor, $a - 6$ .

$\frac{3 (a - 6)}{(a - 6) (a^{2} + 3)}$

Step 4

Cancel the common factor of $a - 6$ .

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Step 4.1

Cancel the common factor.

$\frac{3 (a - 6)}{(a - 6) (a^{2} + 3)}$

Step 4.2

Rewrite the expression.

$\frac{3}{a^{2} + 3}$