Algebra Examples

$\frac{x + 4}{2 x} - \frac{2 x + 1}{6 x}$

Step 1

To write $\frac{x + 4}{2 x}$ as a fraction with a common denominator, multiply by $\frac{3}{3}$ .

$\frac{x + 4}{2 x} \cdot \frac{3}{3} - \frac{2 x + 1}{6 x}$

Step 2

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

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Step 2.1

Multiply $\frac{x + 4}{2 x}$ by $\frac{3}{3}$ .

$\frac{(x + 4) \cdot 3}{2 x \cdot 3} - \frac{2 x + 1}{6 x}$

Step 2.2

Multiply $3$ by $2$ .

$\frac{(x + 4) \cdot 3}{6 x} - \frac{2 x + 1}{6 x}$

Step 3

Combine the numerators over the common denominator.

$\frac{(x + 4) \cdot 3 - (2 x + 1)}{6 x}$

Step 4

Simplify the numerator.

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Step 4.1

Apply the distributive property.

$\frac{x \cdot 3 + 4 \cdot 3 - (2 x + 1)}{6 x}$

Step 4.2

Move $3$ to the left of $x$ .

$\frac{3 \cdot x + 4 \cdot 3 - (2 x + 1)}{6 x}$

Step 4.3

Multiply $4$ by $3$ .

$\frac{3 \cdot x + 12 - (2 x + 1)}{6 x}$

Step 4.4

Apply the distributive property.

$\frac{3 x + 12 - (2 x) - 1 \cdot 1}{6 x}$

Step 4.5

Multiply $2$ by $- 1$ .

$\frac{3 x + 12 - 2 x - 1 \cdot 1}{6 x}$

Step 4.6

Multiply $- 1$ by $1$ .

$\frac{3 x + 12 - 2 x - 1}{6 x}$

Step 4.7

Subtract $2 x$ from $3 x$ .

$\frac{x + 12 - 1}{6 x}$

Step 4.8

Subtract $1$ from $12$ .

$\frac{x + 11}{6 x}$