Basic Math Examples

$\frac{\frac{1}{z} + 3}{\frac{1}{z} - 9}$

Step 1

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

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Step 1.1

Multiply $\frac{\frac{1}{z} + 3}{\frac{1}{z} - 9}$ by $\frac{z}{z}$ .

$\frac{z}{z} \cdot \frac{\frac{1}{z} + 3}{\frac{1}{z} - 9}$

Step 1.2

Combine.

$\frac{z (\frac{1}{z} + 3)}{z (\frac{1}{z} - 9)}$

Step 2

Apply the distributive property.

$\frac{z \frac{1}{z} + z \cdot 3}{z \frac{1}{z} + z \cdot - 9}$

Step 3

Simplify by cancelling.

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Step 3.1

Cancel the common factor of $z$ .

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Step 3.1.1

Cancel the common factor.

$\frac{z \frac{1}{z} + z \cdot 3}{z \frac{1}{z} + z \cdot - 9}$

Step 3.1.2

Rewrite the expression.

$\frac{1 + z \cdot 3}{z \frac{1}{z} + z \cdot - 9}$

Step 3.2

Cancel the common factor of $z$ .

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Step 3.2.1

Cancel the common factor.

$\frac{1 + z \cdot 3}{z \frac{1}{z} + z \cdot - 9}$

Step 3.2.2

Rewrite the expression.

$\frac{1 + z \cdot 3}{1 + z \cdot - 9}$

Step 4

Move $3$ to the left of $z$ .

$\frac{1 + 3 z}{1 + z \cdot - 9}$

Step 5

Move $- 9$ to the left of $z$ .

$\frac{1 + 3 z}{1 - 9 z}$