Basic Math Examples

$\frac{- 5}{z y} - \frac{z^{2}}{y}$

Step 1

Move the negative in front of the fraction.

$- \frac{5}{z y} - \frac{z^{2}}{y}$

Step 2

To write $- \frac{z^{2}}{y}$ as a fraction with a common denominator, multiply by $\frac{z}{z}$ .

$- \frac{5}{z y} - \frac{z^{2}}{y} \cdot \frac{z}{z}$

Step 3

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

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Step 3.1

Multiply $\frac{z^{2}}{y}$ by $\frac{z}{z}$ .

$- \frac{5}{z y} - \frac{z^{2} z}{y z}$

Step 3.2

Reorder the factors of $z y$ .

$- \frac{5}{y z} - \frac{z^{2} z}{y z}$

Step 4

Combine the numerators over the common denominator.

$\frac{- 5 - z^{2} z}{y z}$

Step 5

Multiply $z^{2}$ by $z$ by adding the exponents.

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Step 5.1

Move $z$ .

$\frac{- 5 - (z \cdot z^{2})}{y z}$

Step 5.2

Multiply $z$ by $z^{2}$ .

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Step 5.2.1

Raise $z$ to the power of $1$ .

$\frac{- 5 - (z^{1} z^{2})}{y z}$

Step 5.2.2

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$\frac{- 5 - z^{1 + 2}}{y z}$

Step 5.3

Add $1$ and $2$ .

$\frac{- 5 - z^{3}}{y z}$

Step 6

Rewrite $- 5$ as $- 1 (5)$ .

$\frac{- 1 (5) - z^{3}}{y z}$

Step 7

Factor $- 1$ out of $- z^{3}$ .

$\frac{- 1 (5) - (z^{3})}{y z}$

Step 8

Factor $- 1$ out of $- 1 (5) - (z^{3})$ .

$\frac{- 1 (5 + z^{3})}{y z}$

Step 9

Move the negative in front of the fraction.

$- \frac{5 + z^{3}}{y z}$