Basic Math Examples

$- \frac{7 z + 12 y}{6 z} - \frac{6 z - 6 y}{6 z}$

Step 1

Combine the numerators over the common denominator.

$\frac{- (7 z + 12 y) - (6 z - 6 y)}{6 z}$

Step 2

Simplify each term.

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Step 2.1

Apply the distributive property.

$\frac{- (7 z) - (12 y) - (6 z - 6 y)}{6 z}$

Step 2.2

Multiply $7$ by $- 1$ .

$\frac{- 7 z - (12 y) - (6 z - 6 y)}{6 z}$

Step 2.3

Multiply $12$ by $- 1$ .

$\frac{- 7 z - 12 y - (6 z - 6 y)}{6 z}$

Step 2.4

Apply the distributive property.

$\frac{- 7 z - 12 y - (6 z) - (- 6 y)}{6 z}$

Step 2.5

Multiply $6$ by $- 1$ .

$\frac{- 7 z - 12 y - 6 z - (- 6 y)}{6 z}$

Step 2.6

Multiply $- 6$ by $- 1$ .

$\frac{- 7 z - 12 y - 6 z + 6 y}{6 z}$

$\frac{- 7 z - 12 y - 6 z + 6 y}{6 z}$

Step 3

Simplify terms.

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Step 3.1

Subtract $6 z$ from $- 7 z$ .

$\frac{- 12 y - 13 z + 6 y}{6 z}$

Step 3.2

Add $- 12 y$ and $6 y$ .

$\frac{- 6 y - 13 z}{6 z}$

Step 3.3

Factor $- 1$ out of $- 6 y$ .

$\frac{- (6 y) - 13 z}{6 z}$

Step 3.4

Factor $- 1$ out of $- 13 z$ .

$\frac{- (6 y) - (13 z)}{6 z}$

Step 3.5

Factor $- 1$ out of $- (6 y) - (13 z)$ .

$\frac{- (6 y + 13 z)}{6 z}$

Step 3.6

Simplify the expression.

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Step 3.6.1

Rewrite $- (6 y + 13 z)$ as $- 1 (6 y + 13 z)$ .

$\frac{- 1 (6 y + 13 z)}{6 z}$

Step 3.6.2

Move the negative in front of the fraction.

$- \frac{6 y + 13 z}{6 z}$

$- \frac{6 y + 13 z}{6 z}$

$- \frac{6 y + 13 z}{6 z}$

$[\begin{array}{c} x^{2} & \frac{1}{2} \\ \sqrt{π} & \int x d x \end{array}]$