Algebra Examples

$- \frac{8}{27} - \frac{5}{9 x}$

Step 1

To write $- \frac{8}{27}$ as a fraction with a common denominator, multiply by $\frac{x}{x}$ .

$- \frac{8}{27} \cdot \frac{x}{x} - \frac{5}{9 x}$

Step 2

To write $- \frac{5}{9 x}$ as a fraction with a common denominator, multiply by $\frac{3}{3}$ .

$- \frac{8}{27} \cdot \frac{x}{x} - \frac{5}{9 x} \cdot \frac{3}{3}$

Step 3

Write each expression with a common denominator of $27 x$ , by multiplying each by an appropriate factor of $1$ .

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Step 3.1

Multiply $\frac{8}{27}$ by $\frac{x}{x}$ .

$- \frac{8 x}{27 x} - \frac{5}{9 x} \cdot \frac{3}{3}$

Step 3.2

Multiply $\frac{5}{9 x}$ by $\frac{3}{3}$ .

$- \frac{8 x}{27 x} - \frac{5 \cdot 3}{9 x \cdot 3}$

Step 3.3

Multiply $3$ by $9$ .

$- \frac{8 x}{27 x} - \frac{5 \cdot 3}{27 x}$

Step 4

Combine the numerators over the common denominator.

$\frac{- 8 x - 5 \cdot 3}{27 x}$

Step 5

Multiply $- 5$ by $3$ .

$\frac{- 8 x - 15}{27 x}$

Step 6

Factor $- 1$ out of $- 8 x$ .

$\frac{- (8 x) - 15}{27 x}$

Step 7

Rewrite $- 15$ as $- 1 (15)$ .

$\frac{- (8 x) - 1 (15)}{27 x}$

Step 8

Factor $- 1$ out of $- (8 x) - 1 (15)$ .

$\frac{- (8 x + 15)}{27 x}$

Step 9

Simplify the expression.

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Step 9.1

Rewrite $- (8 x + 15)$ as $- 1 (8 x + 15)$ .

$\frac{- 1 (8 x + 15)}{27 x}$

Step 9.2

Move the negative in front of the fraction.

$- \frac{8 x + 15}{27 x}$