Basic Math Examples

$\frac{\frac{2 z^{3}}{z^{2} - 9}}{\frac{z^{6}}{{(z + 3)}^{2}}}$

Step 1

Multiply the numerator by the reciprocal of the denominator.

$\frac{2 z^{3}}{z^{2} - 9} \cdot \frac{{(z + 3)}^{2}}{z^{6}}$

Step 2

Simplify terms.

Tap for more steps...

Step 2.1

Cancel the common factor of $z^{3}$ .

Tap for more steps...

Step 2.1.1

Factor $z^{3}$ out of $2 z^{3}$ .

$\frac{z^{3} \cdot 2}{z^{2} - 9} \cdot \frac{{(z + 3)}^{2}}{z^{6}}$

Step 2.1.2

Factor $z^{3}$ out of $z^{6}$ .

$\frac{z^{3} \cdot 2}{z^{2} - 9} \cdot \frac{{(z + 3)}^{2}}{z^{3} z^{3}}$

Step 2.1.3

Cancel the common factor.

$\frac{z^{3} \cdot 2}{z^{2} - 9} \cdot \frac{{(z + 3)}^{2}}{z^{3} z^{3}}$

Step 2.1.4

Rewrite the expression.

$\frac{2}{z^{2} - 9} \cdot \frac{{(z + 3)}^{2}}{z^{3}}$

Step 2.2

Multiply $\frac{2}{z^{2} - 9}$ by $\frac{{(z + 3)}^{2}}{z^{3}}$ .

$\frac{2 {(z + 3)}^{2}}{(z^{2} - 9) z^{3}}$

Step 3

Simplify the denominator.

Tap for more steps...

Step 3.1

Rewrite $9$ as $3^{2}$ .

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

Step 3.2

Since both terms are perfect squares, factor using the difference of squares formula, $a^{2} - b^{2} = (a + b) (a - b)$ where $a = z$ and $b = 3$ .

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

Step 4

Reduce the expression by cancelling the common factors.

Tap for more steps...

Step 4.1

Cancel the common factor of ${(z + 3)}^{2}$ and $z + 3$ .

Tap for more steps...

Step 4.1.1

Factor $z + 3$ out of $2 {(z + 3)}^{2}$ .

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

Step 4.1.2

Cancel the common factors.

Tap for more steps...

Step 4.1.2.1

Factor $z + 3$ out of $(z + 3) (z - 3) z^{3}$ .

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

Step 4.1.2.2

Cancel the common factor.

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

Step 4.1.2.3

Rewrite the expression.

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

Step 4.2

Reorder factors in $\frac{2 (z + 3)}{(z - 3) z^{3}}$ .

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