Calculus Examples

$- \frac{7}{6} - \frac{1}{3 x}$

Step 1

To write $- \frac{7}{6}$ as a fraction with a common denominator, multiply by $\frac{x}{x}$ .

$- \frac{7}{6} \cdot \frac{x}{x} - \frac{1}{3 x}$

Step 2

To write $- \frac{1}{3 x}$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$- \frac{7}{6} \cdot \frac{x}{x} - \frac{1}{3 x} \cdot \frac{2}{2}$

Step 3

Write each expression with a common denominator of $6 x$ , by multiplying each by an appropriate factor of $1$ .

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Step 3.1

Multiply $\frac{7}{6}$ by $\frac{x}{x}$ .

$- \frac{7 x}{6 x} - \frac{1}{3 x} \cdot \frac{2}{2}$

Step 3.2

Multiply $\frac{1}{3 x}$ by $\frac{2}{2}$ .

$- \frac{7 x}{6 x} - \frac{2}{3 x \cdot 2}$

Step 3.3

Multiply $2$ by $3$ .

$- \frac{7 x}{6 x} - \frac{2}{6 x}$

Step 4

Combine the numerators over the common denominator.

$\frac{- 7 x - 2}{6 x}$

Step 5

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

$\frac{- (7 x) - 2}{6 x}$

Step 6

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

$\frac{- (7 x) - 1 (2)}{6 x}$

Step 7

Factor $- 1$ out of $- (7 x) - 1 (2)$ .

$\frac{- (7 x + 2)}{6 x}$

Step 8

Simplify the expression.

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Step 8.1

Rewrite $- (7 x + 2)$ as $- 1 (7 x + 2)$ .

$\frac{- 1 (7 x + 2)}{6 x}$

Step 8.2

Move the negative in front of the fraction.

$- \frac{7 x + 2}{6 x}$