Simplify (1/2x-3)+(1/6x+1)

$(\frac{1}{2} x - 3) + (\frac{1}{6} x + 1)$

Step 1

Remove parentheses.

$\frac{1}{2} x - 3 + \frac{1}{6} x + 1$

Step 2

Simplify each term.

Combine $\frac{1}{2}$ and $x$ .

$\frac{x}{2} - 3 + \frac{1}{6} x + 1$

Combine $\frac{1}{6}$ and $x$ .

$\frac{x}{2} - 3 + \frac{x}{6} + 1$

Step 3

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

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

Step 4

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

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

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

Multiply $2$ by $3$ .

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

Step 5

Combine the numerators over the common denominator.

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

Step 6

Add $x \cdot 3$ and $x$ .

Reorder $x$ and $3$ .

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

Add $3 \cdot x$ and $x$ .

$\frac{4 \cdot x}{6} - 3 + 1$

Step 7

Cancel the common factor of $4$ and $6$ .

Factor $2$ out of $4 \cdot x$ .

$\frac{2 (2 \cdot x)}{6} - 3 + 1$

Cancel the common factors.

Factor $2$ out of $6$ .

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

Cancel the common factor.

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

Rewrite the expression.

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

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

Step 8

Add $- 3$ and $1$ .

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