Basic Math Examples

$\frac{1}{z} - \frac{z - 7}{2}$

Step 1

To write $\frac{1}{z}$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$\frac{1}{z} \cdot \frac{2}{2} - \frac{z - 7}{2}$

Step 2

To write $- \frac{z - 7}{2}$ as a fraction with a common denominator, multiply by $\frac{z}{z}$ .

$\frac{1}{z} \cdot \frac{2}{2} - \frac{z - 7}{2} \cdot \frac{z}{z}$

Step 3

Write each expression with a common denominator of $z \cdot 2$ , by multiplying each by an appropriate factor of $1$ .

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Step 3.1

Multiply $\frac{1}{z}$ by $\frac{2}{2}$ .

$\frac{2}{z \cdot 2} - \frac{z - 7}{2} \cdot \frac{z}{z}$

Step 3.2

Multiply $\frac{z - 7}{2}$ by $\frac{z}{z}$ .

$\frac{2}{z \cdot 2} - \frac{(z - 7) z}{2 z}$

Step 3.3

Reorder the factors of $z \cdot 2$ .

$\frac{2}{2 z} - \frac{(z - 7) z}{2 z}$

Step 4

Combine the numerators over the common denominator.

$\frac{2 - (z - 7) z}{2 z}$

Step 5

Simplify the numerator.

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Step 5.1

Apply the distributive property.

$\frac{2 + (- z - - 7) z}{2 z}$

Step 5.2

Multiply $- 1$ by $- 7$ .

$\frac{2 + (- z + 7) z}{2 z}$

Step 5.3

Apply the distributive property.

$\frac{2 - z \cdot z + 7 z}{2 z}$

Step 5.4

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

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Step 5.4.1

Move $z$ .

$\frac{2 - (z \cdot z) + 7 z}{2 z}$

Step 5.4.2

Multiply $z$ by $z$ .

$\frac{2 - z^{2} + 7 z}{2 z}$

Step 5.5

Reorder terms.

$\frac{- z^{2} + 7 z + 2}{2 z}$

Step 6

Simplify with factoring out.

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Step 6.1

Factor $- 1$ out of $- z^{2}$ .

$\frac{- (z^{2}) + 7 z + 2}{2 z}$

Step 6.2

Factor $- 1$ out of $7 z$ .

$\frac{- (z^{2}) - (- 7 z) + 2}{2 z}$

Step 6.3

Factor $- 1$ out of $- (z^{2}) - (- 7 z)$ .

$\frac{- (z^{2} - 7 z) + 2}{2 z}$

Step 6.4

Rewrite $2$ as $- 1 (- 2)$ .

$\frac{- (z^{2} - 7 z) - 1 (- 2)}{2 z}$

Step 6.5

Factor $- 1$ out of $- (z^{2} - 7 z) - 1 (- 2)$ .

$\frac{- (z^{2} - 7 z - 2)}{2 z}$

Step 6.6

Simplify the expression.

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Step 6.6.1

Rewrite $- (z^{2} - 7 z - 2)$ as $- 1 (z^{2} - 7 z - 2)$ .

$\frac{- 1 (z^{2} - 7 z - 2)}{2 z}$

Step 6.6.2

Move the negative in front of the fraction.

$- \frac{z^{2} - 7 z - 2}{2 z}$