Basic Math Examples

$\frac{5}{z + 6} + \frac{1}{z}$

Step 1

To write $\frac{5}{z + 6}$ as a fraction with a common denominator, multiply by $\frac{z}{z}$ .

$\frac{5}{z + 6} \cdot \frac{z}{z} + \frac{1}{z}$

Step 2

To write $\frac{1}{z}$ as a fraction with a common denominator, multiply by $\frac{z + 6}{z + 6}$ .

$\frac{5}{z + 6} \cdot \frac{z}{z} + \frac{1}{z} \cdot \frac{z + 6}{z + 6}$

Step 3

Write each expression with a common denominator of $(z + 6) z$ , by multiplying each by an appropriate factor of $1$ .

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Step 3.1

Multiply $\frac{5}{z + 6}$ by $\frac{z}{z}$ .

$\frac{5 z}{(z + 6) z} + \frac{1}{z} \cdot \frac{z + 6}{z + 6}$

Step 3.2

Multiply $\frac{1}{z}$ by $\frac{z + 6}{z + 6}$ .

$\frac{5 z}{(z + 6) z} + \frac{z + 6}{z (z + 6)}$

Step 3.3

Reorder the factors of $(z + 6) z$ .

$\frac{5 z}{z (z + 6)} + \frac{z + 6}{z (z + 6)}$

Step 4

Combine the numerators over the common denominator.

$\frac{5 z + z + 6}{z (z + 6)}$

Step 5

Simplify the numerator.

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Step 5.1

Add $5 z$ and $z$ .

$\frac{6 z + 6}{z (z + 6)}$

Step 5.2

Factor $6$ out of $6 z + 6$ .

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Step 5.2.1

Factor $6$ out of $6 z$ .

$\frac{6 (z) + 6}{z (z + 6)}$

Step 5.2.2

Factor $6$ out of $6$ .

$\frac{6 (z) + 6 (1)}{z (z + 6)}$

Step 5.2.3

Factor $6$ out of $6 (z) + 6 (1)$ .

$\frac{6 (z + 1)}{z (z + 6)}$