Simplify (4x-1)/(5x)-(2x+2)/(15x)

$\frac{4 x - 1}{5 x} - \frac{2 x + 2}{15 x}$

Step 1

Factor $2$ out of $2 x + 2$ .

Factor $2$ out of $2 x$ .

$\frac{4 x - 1}{5 x} - \frac{2 (x) + 2}{15 x}$

Factor $2$ out of $2$ .

$\frac{4 x - 1}{5 x} - \frac{2 (x) + 2 (1)}{15 x}$

Factor $2$ out of $2 (x) + 2 (1)$ .

$\frac{4 x - 1}{5 x} - \frac{2 (x + 1)}{15 x}$

Step 2

To write $\frac{4 x - 1}{5 x}$ as a fraction with a common denominator, multiply by $\frac{3}{3}$ .

$\frac{4 x - 1}{5 x} \cdot \frac{3}{3} - \frac{2 (x + 1)}{15 x}$

Step 3

Write each expression with a common denominator of $15 x$ , by multiplying each by an appropriate factor of $1$ .

Multiply $\frac{4 x - 1}{5 x}$ by $\frac{3}{3}$ .

$\frac{(4 x - 1) \cdot 3}{5 x \cdot 3} - \frac{2 (x + 1)}{15 x}$

Multiply $3$ by $5$ .

$\frac{(4 x - 1) \cdot 3}{15 x} - \frac{2 (x + 1)}{15 x}$

Step 4

Combine the numerators over the common denominator.

$\frac{(4 x - 1) \cdot 3 - 2 (x + 1)}{15 x}$

Step 5

Simplify the numerator.

Apply the distributive property.

$\frac{4 x \cdot 3 - 1 \cdot 3 - 2 (x + 1)}{15 x}$

Multiply $3$ by $4$ .

$\frac{12 x - 1 \cdot 3 - 2 (x + 1)}{15 x}$

Multiply $- 1$ by $3$ .

$\frac{12 x - 3 - 2 (x + 1)}{15 x}$

Apply the distributive property.

$\frac{12 x - 3 - 2 x - 2 \cdot 1}{15 x}$

Multiply $- 2$ by $1$ .

$\frac{12 x - 3 - 2 x - 2}{15 x}$

Subtract $2 x$ from $12 x$ .

$\frac{10 x - 3 - 2}{15 x}$

Subtract $2$ from $- 3$ .

$\frac{10 x - 5}{15 x}$

Factor $5$ out of $10 x - 5$ .

Factor $5$ out of $10 x$ .

$\frac{5 (2 x) - 5}{15 x}$

Factor $5$ out of $- 5$ .

$\frac{5 (2 x) + 5 (- 1)}{15 x}$

Factor $5$ out of $5 (2 x) + 5 (- 1)$ .

$\frac{5 (2 x - 1)}{15 x}$

Step 6

Cancel the common factors.

Factor $5$ out of $15 x$ .

$\frac{5 (2 x - 1)}{5 (3 x)}$

Cancel the common factor.

$\frac{5 (2 x - 1)}{5 (3 x)}$

Rewrite the expression.

$\frac{2 x - 1}{3 x}$

Simplify (4x-1)/(5x)-(2x+2)/(15x)

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