Basic Math Examples

$\frac{\frac{2}{w} + \frac{3}{z}}{\frac{3}{w} - \frac{2}{z}}$

Step 1

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

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Step 1.1

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

$\frac{w z}{w z} \cdot \frac{\frac{2}{w} + \frac{3}{z}}{\frac{3}{w} - \frac{2}{z}}$

Step 1.2

Combine.

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

Step 2

Apply the distributive property.

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

Step 3

Simplify by cancelling.

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Step 3.1

Cancel the common factor of $w$ .

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Step 3.1.1

Factor $w$ out of $w z$ .

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

Step 3.1.2

Cancel the common factor.

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

Step 3.1.3

Rewrite the expression.

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

Step 3.2

Cancel the common factor of $z$ .

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Step 3.2.1

Factor $z$ out of $w z$ .

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

Step 3.2.2

Cancel the common factor.

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

Step 3.2.3

Rewrite the expression.

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

Step 3.3

Cancel the common factor of $w$ .

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Step 3.3.1

Factor $w$ out of $w z$ .

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

Step 3.3.2

Cancel the common factor.

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

Step 3.3.3

Rewrite the expression.

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

Step 3.4

Cancel the common factor of $z$ .

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Step 3.4.1

Move the leading negative in $- \frac{2}{z}$ into the numerator.

$\frac{z \cdot 2 + w \cdot 3}{z \cdot 3 + w z \frac{- 2}{z}}$

Step 3.4.2

Factor $z$ out of $w z$ .

$\frac{z \cdot 2 + w \cdot 3}{z \cdot 3 + z w \frac{- 2}{z}}$

Step 3.4.3

Cancel the common factor.

$\frac{z \cdot 2 + w \cdot 3}{z \cdot 3 + z w \frac{- 2}{z}}$

Step 3.4.4

Rewrite the expression.

$\frac{z \cdot 2 + w \cdot 3}{z \cdot 3 + w \cdot - 2}$

Step 4

Simplify the numerator.

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Step 4.1

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

$\frac{2 \cdot z + w \cdot 3}{z \cdot 3 + w \cdot - 2}$

Step 4.2

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

$\frac{2 z + 3 w}{z \cdot 3 + w \cdot - 2}$

Step 5

Simplify the denominator.

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Step 5.1

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

$\frac{2 z + 3 w}{3 \cdot z + w \cdot - 2}$

Step 5.2

Move $- 2$ to the left of $w$ .

$\frac{2 z + 3 w}{3 z - 2 w}$