Basic Math Examples

$\frac{z - \frac{z - 3}{3}}{\frac{4}{9} + \frac{2}{3 z}}$

Step 1

Multiply the numerator and denominator of the fraction by $9 z$ .

Tap for more steps...

Step 1.1

Multiply $\frac{z - \frac{z - 3}{3}}{\frac{4}{9} + \frac{2}{3 z}}$ by $\frac{9 z}{9 z}$ .

$\frac{9 z}{9 z} \cdot \frac{z - \frac{z - 3}{3}}{\frac{4}{9} + \frac{2}{3 z}}$

Step 1.2

Combine.

$\frac{9 z (z - \frac{z - 3}{3})}{9 z (\frac{4}{9} + \frac{2}{3 z})}$

Step 2

Apply the distributive property.

$\frac{9 z \cdot z + 9 z (- \frac{z - 3}{3})}{9 z \frac{4}{9} + 9 z \frac{2}{3 z}}$

Step 3

Simplify by cancelling.

Tap for more steps...

Step 3.1

Cancel the common factor of $3$ .

Tap for more steps...

Step 3.1.1

Move the leading negative in $- \frac{z - 3}{3}$ into the numerator.

$\frac{9 z \cdot z + 9 z \frac{- (z - 3)}{3}}{9 z \frac{4}{9} + 9 z \frac{2}{3 z}}$

Step 3.1.2

Factor $3$ out of $9 z$ .

$\frac{9 z \cdot z + 3 (3 z) \frac{- (z - 3)}{3}}{9 z \frac{4}{9} + 9 z \frac{2}{3 z}}$

Step 3.1.3

Cancel the common factor.

$\frac{9 z \cdot z + 3 (3 z) \frac{- (z - 3)}{3}}{9 z \frac{4}{9} + 9 z \frac{2}{3 z}}$

Step 3.1.4

Rewrite the expression.

$\frac{9 z \cdot z + 3 z (- (z - 3))}{9 z \frac{4}{9} + 9 z \frac{2}{3 z}}$

Step 3.2

Multiply $- 1$ by $3$ .

$\frac{9 z \cdot z - 3 z (z - 3)}{9 z \frac{4}{9} + 9 z \frac{2}{3 z}}$

Step 3.3

Cancel the common factor of $9$ .

Tap for more steps...

Step 3.3.1

Factor $9$ out of $9 z$ .

$\frac{9 z \cdot z - 3 z (z - 3)}{9 (z) \frac{4}{9} + 9 z \frac{2}{3 z}}$

Step 3.3.2

Cancel the common factor.

$\frac{9 z \cdot z - 3 z (z - 3)}{9 z \frac{4}{9} + 9 z \frac{2}{3 z}}$

Step 3.3.3

Rewrite the expression.

$\frac{9 z \cdot z - 3 z (z - 3)}{z \cdot 4 + 9 z \frac{2}{3 z}}$

Step 3.4

Cancel the common factor of $3 z$ .

Tap for more steps...

Step 3.4.1

Factor $3 z$ out of $9 z$ .

$\frac{9 z \cdot z - 3 z (z - 3)}{z \cdot 4 + 3 z (3) \frac{2}{3 z}}$

Step 3.4.2

Cancel the common factor.

$\frac{9 z \cdot z - 3 z (z - 3)}{z \cdot 4 + 3 z \cdot 3 \frac{2}{3 z}}$

Step 3.4.3

Rewrite the expression.

$\frac{9 z \cdot z - 3 z (z - 3)}{z \cdot 4 + 3 \cdot 2}$

Step 3.5

Multiply $3$ by $2$ .

$\frac{9 z \cdot z - 3 z (z - 3)}{z \cdot 4 + 6}$

Step 4

Simplify the numerator.

Tap for more steps...

Step 4.1

Multiply $z$ by $z$ by adding the exponents.

Tap for more steps...

Step 4.1.1

Move $z$ .

$\frac{9 (z \cdot z) - 3 z (z - 3)}{z \cdot 4 + 6}$

Step 4.1.2

Multiply $z$ by $z$ .

$\frac{9 z^{2} - 3 z (z - 3)}{z \cdot 4 + 6}$

Step 4.2

Apply the distributive property.

$\frac{9 z^{2} - 3 z \cdot z - 3 z \cdot - 3}{z \cdot 4 + 6}$

Step 4.3

Multiply $z$ by $z$ by adding the exponents.

Tap for more steps...

Step 4.3.1

Move $z$ .

$\frac{9 z^{2} - 3 (z \cdot z) - 3 z \cdot - 3}{z \cdot 4 + 6}$

Step 4.3.2

Multiply $z$ by $z$ .

$\frac{9 z^{2} - 3 z^{2} - 3 z \cdot - 3}{z \cdot 4 + 6}$

Step 4.4

Multiply $- 3$ by $- 3$ .

$\frac{9 z^{2} - 3 z^{2} + 9 z}{z \cdot 4 + 6}$

Step 4.5

Subtract $3 z^{2}$ from $9 z^{2}$ .

$\frac{6 z^{2} + 9 z}{z \cdot 4 + 6}$

Step 4.6

Factor $3 z$ out of $6 z^{2} + 9 z$ .

Tap for more steps...

Step 4.6.1

Factor $3 z$ out of $6 z^{2}$ .

$\frac{3 z (2 z) + 9 z}{z \cdot 4 + 6}$

Step 4.6.2

Factor $3 z$ out of $9 z$ .

$\frac{3 z (2 z) + 3 z (3)}{z \cdot 4 + 6}$

Step 4.6.3

Factor $3 z$ out of $3 z (2 z) + 3 z (3)$ .

$\frac{3 z (2 z + 3)}{z \cdot 4 + 6}$

Step 5

Simplify the denominator.

Tap for more steps...

Step 5.1

Factor $2$ out of $z \cdot 4 + 6$ .

Tap for more steps...

Step 5.1.1

Factor $2$ out of $z \cdot 4$ .

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

Step 5.1.2

Factor $2$ out of $6$ .

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

Step 5.1.3

Factor $2$ out of $2 (z \cdot 2) + 2 (3)$ .

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

Step 5.2

Move $2$ to the left of $z$ .

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

Step 6

Cancel the common factor of $2 z + 3$ .

Tap for more steps...

Step 6.1

Cancel the common factor.

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

Step 6.2

Rewrite the expression.

$\frac{3 z}{2}$