Basic Math Examples

$\frac{\frac{4}{z} - \frac{4}{5}}{z - 5}$

Step 1

Multiply the numerator and denominator of the fraction by $z \cdot 5$ .

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Step 1.1

Multiply $\frac{\frac{4}{z} - \frac{4}{5}}{z - 5}$ by $\frac{z \cdot 5}{z \cdot 5}$ .

$\frac{z \cdot 5}{z \cdot 5} \cdot \frac{\frac{4}{z} - \frac{4}{5}}{z - 5}$

Step 1.2

Combine.

$\frac{z \cdot 5 (\frac{4}{z} - \frac{4}{5})}{z \cdot 5 (z - 5)}$

Step 2

Apply the distributive property.

$\frac{z \cdot 5 \frac{4}{z} + z \cdot 5 (- \frac{4}{5})}{z \cdot 5 z + z \cdot 5 \cdot - 5}$

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

Factor $z$ out of $z \cdot 5$ .

$\frac{z (5) \frac{4}{z} + z \cdot 5 (- \frac{4}{5})}{z \cdot 5 z + z \cdot 5 \cdot - 5}$

Step 3.1.2

Cancel the common factor.

$\frac{z \cdot 5 \frac{4}{z} + z \cdot 5 (- \frac{4}{5})}{z \cdot 5 z + z \cdot 5 \cdot - 5}$

Step 3.1.3

Rewrite the expression.

$\frac{5 \cdot 4 + z \cdot 5 (- \frac{4}{5})}{z \cdot 5 z + z \cdot 5 \cdot - 5}$

Step 3.2

Multiply $5$ by $4$ .

$\frac{20 + z \cdot 5 (- \frac{4}{5})}{z \cdot 5 z + z \cdot 5 \cdot - 5}$

Step 3.3

Cancel the common factor of $5$ .

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Step 3.3.1

Move the leading negative in $- \frac{4}{5}$ into the numerator.

$\frac{20 + z \cdot 5 \frac{- 4}{5}}{z \cdot 5 z + z \cdot 5 \cdot - 5}$

Step 3.3.2

Factor $5$ out of $z \cdot 5$ .

$\frac{20 + 5 \cdot z \frac{- 4}{5}}{z \cdot 5 z + z \cdot 5 \cdot - 5}$

Step 3.3.3

Cancel the common factor.

$\frac{20 + 5 \cdot z \frac{- 4}{5}}{z \cdot 5 z + z \cdot 5 \cdot - 5}$

Step 3.3.4

Rewrite the expression.

$\frac{20 + z \cdot - 4}{z \cdot 5 z + z \cdot 5 \cdot - 5}$

Step 4

Simplify the numerator.

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Step 4.1

Factor $4$ out of $20 + z \cdot - 4$ .

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Step 4.1.1

Factor $4$ out of $20$ .

$\frac{4 (5) + z \cdot - 4}{z \cdot 5 z + z \cdot 5 \cdot - 5}$

Step 4.1.2

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

$\frac{4 (5) + 4 (z \cdot - 1)}{z \cdot 5 z + z \cdot 5 \cdot - 5}$

Step 4.1.3

Factor $4$ out of $4 (5) + 4 (z \cdot - 1)$ .

$\frac{4 (5 + z \cdot - 1)}{z \cdot 5 z + z \cdot 5 \cdot - 5}$

Step 4.2

Move $- 1$ to the left of $z$ .

$\frac{4 (5 - 1 \cdot z)}{z \cdot 5 z + z \cdot 5 \cdot - 5}$

Step 4.3

Rewrite $- 1 z$ as $- z$ .

$\frac{4 (5 - z)}{z \cdot 5 z + z \cdot 5 \cdot - 5}$

Step 5

Simplify the denominator.

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Step 5.1

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

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Step 5.1.1

Move $z$ .

$\frac{4 (5 - z)}{z \cdot z \cdot 5 + z \cdot 5 \cdot - 5}$

Step 5.1.2

Multiply $z$ by $z$ .

$\frac{4 (5 - z)}{z^{2} \cdot 5 + z \cdot 5 \cdot - 5}$

Step 5.2

Move $5$ to the left of $z^{2}$ .

$\frac{4 (5 - z)}{5 \cdot z^{2} + z \cdot 5 \cdot - 5}$

Step 5.3

Move $5$ to the left of $z$ .

$\frac{4 (5 - z)}{5 z^{2} + 5 \cdot z \cdot - 5}$

Step 5.4

Multiply $- 5$ by $5$ .

$\frac{4 (5 - z)}{5 z^{2} - 25 z}$

Step 5.5

Factor $5 z$ out of $5 z^{2} - 25 z$ .

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Step 5.5.1

Factor $5 z$ out of $5 z^{2}$ .

$\frac{4 (5 - z)}{5 z (z) - 25 z}$

Step 5.5.2

Factor $5 z$ out of $- 25 z$ .

$\frac{4 (5 - z)}{5 z (z) + 5 z (- 5)}$

Step 5.5.3

Factor $5 z$ out of $5 z (z) + 5 z (- 5)$ .

$\frac{4 (5 - z)}{5 z (z - 5)}$

Step 6

Cancel the common factor of $5 - z$ and $z - 5$ .

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Step 6.1

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

$\frac{4 (- 1 (- 5) - z)}{5 z (z - 5)}$

Step 6.2

Factor $- 1$ out of $- z$ .

$\frac{4 (- 1 (- 5) - (z))}{5 z (z - 5)}$

Step 6.3

Factor $- 1$ out of $- 1 (- 5) - (z)$ .

$\frac{4 (- 1 (- 5 + z))}{5 z (z - 5)}$

Step 6.4

Reorder terms.

$\frac{4 (- 1 (z - 5))}{5 z (z - 5)}$

Step 6.5

Cancel the common factor.

$\frac{4 (- 1 (z - 5))}{5 z (z - 5)}$

Step 6.6

Rewrite the expression.

$\frac{4 \cdot (- 1)}{5 z}$

Step 7

Multiply $4$ by $- 1$ .

$\frac{- 4}{5 z}$

Step 8

Move the negative in front of the fraction.

$- \frac{4}{5 z}$