Algebra Examples

$\frac{x - 6}{x} - \frac{7}{2 x}$

Step 1

To write $\frac{x - 6}{x}$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$\frac{x - 6}{x} \cdot \frac{2}{2} - \frac{7}{2 x}$

Step 2

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

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Step 2.1

Multiply $\frac{x - 6}{x}$ by $\frac{2}{2}$ .

$\frac{(x - 6) \cdot 2}{x \cdot 2} - \frac{7}{2 x}$

Step 2.2

Move $2$ to the left of $x$ .

$\frac{(x - 6) \cdot 2}{2 x} - \frac{7}{2 x}$

Step 3

Combine the numerators over the common denominator.

$\frac{(x - 6) \cdot 2 - 7}{2 x}$

Step 4

Simplify the numerator.

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Step 4.1

Apply the distributive property.

$\frac{x \cdot 2 - 6 \cdot 2 - 7}{2 x}$

Step 4.2

Move $2$ to the left of $x$ .

$\frac{2 \cdot x - 6 \cdot 2 - 7}{2 x}$

Step 4.3

Multiply $- 6$ by $2$ .

$\frac{2 \cdot x - 12 - 7}{2 x}$

Step 4.4

Subtract $7$ from $- 12$ .

$\frac{2 x - 19}{2 x}$