Basic Math Examples

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

Step 1

Multiply the numerator by the reciprocal of the denominator.

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

Step 2

To write $\frac{1}{3 z}$ as a fraction with a common denominator, multiply by $\frac{y}{y}$ .

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

Step 3

To write $- \frac{1}{3 y}$ as a fraction with a common denominator, multiply by $\frac{z}{z}$ .

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

Step 4

Write each expression with a common denominator of $3 z y$ , by multiplying each by an appropriate factor of $1$ .

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Step 4.1

Multiply $\frac{1}{3 z}$ by $\frac{y}{y}$ .

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

Step 4.2

Multiply $\frac{1}{3 y}$ by $\frac{z}{z}$ .

$(\frac{y}{3 z y} - \frac{z}{3 y z}) (z + y)$

Step 4.3

Reorder the factors of $3 z y$ .

$(\frac{y}{3 y z} - \frac{z}{3 y z}) (z + y)$

Step 5

Combine the numerators over the common denominator.

$\frac{y - z}{3 y z} (z + y)$

Step 6

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

$\frac{(y - z) (z + y)}{3 y z}$