Simplify (2x)/(4xy)-6/(2x)

$\frac{2 x}{4 x y} - \frac{6}{2 x}$

Step 1

Simplify each term.

Cancel the common factor of $2$ and $4$ .

Factor $2$ out of $2 x$ .

$\frac{2 (x)}{4 x y} - \frac{6}{2 x}$

Cancel the common factors.

Factor $2$ out of $4 x y$ .

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

Cancel the common factor.

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

Rewrite the expression.

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

Cancel the common factor of $x$ .

Cancel the common factor.

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

Rewrite the expression.

$\frac{1}{2 y} - \frac{6}{2 x}$

Cancel the common factor of $6$ and $2$ .

Factor $2$ out of $6$ .

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

Cancel the common factors.

Factor $2$ out of $2 x$ .

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

Cancel the common factor.

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

Rewrite the expression.

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

Step 2

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

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

Step 3

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

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

Step 4

Write each expression with a common denominator of $2 y x$ , by multiplying each by an appropriate factor of $1$ .

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

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

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

$\frac{x}{2 y x} - \frac{3 (2 y)}{x (2 y)}$

Reorder the factors of $2 y x$ .

$\frac{x}{2 x y} - \frac{3 (2 y)}{x (2 y)}$

Reorder the factors of $x (2 y)$ .

$\frac{x}{2 x y} - \frac{3 (2 y)}{2 x y}$

Step 5

Combine the numerators over the common denominator.

$\frac{x - 3 (2 y)}{2 x y}$

Step 6

Multiply $- 3$ by $2$ .

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

Simplify (2x)/(4xy)-6/(2x)

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