Algebra Examples

$\frac{x - 5}{4 x} - \frac{2 x + 6}{16 x}$

Step 1

Cancel the common factor of $2 x + 6$ and $16$ .

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Step 1.1

Factor $2$ out of $2 x$ .

$\frac{x - 5}{4 x} - \frac{2 (x) + 6}{16 x}$

Step 1.2

Factor $2$ out of $6$ .

$\frac{x - 5}{4 x} - \frac{2 x + 2 \cdot 3}{16 x}$

Step 1.3

Factor $2$ out of $2 x + 2 \cdot 3$ .

$\frac{x - 5}{4 x} - \frac{2 (x + 3)}{16 x}$

Step 1.4

Cancel the common factors.

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Step 1.4.1

Factor $2$ out of $16 x$ .

$\frac{x - 5}{4 x} - \frac{2 (x + 3)}{2 (8 x)}$

Step 1.4.2

Cancel the common factor.

$\frac{x - 5}{4 x} - \frac{2 (x + 3)}{2 (8 x)}$

Step 1.4.3

Rewrite the expression.

$\frac{x - 5}{4 x} - \frac{x + 3}{8 x}$

Step 2

To write $\frac{x - 5}{4 x}$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$\frac{x - 5}{4 x} \cdot \frac{2}{2} - \frac{x + 3}{8 x}$

Step 3

Write each expression with a common denominator of $8 x$ , by multiplying each by an appropriate factor of $1$ .

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Step 3.1

Multiply $\frac{x - 5}{4 x}$ by $\frac{2}{2}$ .

$\frac{(x - 5) \cdot 2}{4 x \cdot 2} - \frac{x + 3}{8 x}$

Step 3.2

Multiply $2$ by $4$ .

$\frac{(x - 5) \cdot 2}{8 x} - \frac{x + 3}{8 x}$

Step 4

Combine the numerators over the common denominator.

$\frac{(x - 5) \cdot 2 - (x + 3)}{8 x}$

Step 5

Simplify the numerator.

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Step 5.1

Apply the distributive property.

$\frac{x \cdot 2 - 5 \cdot 2 - (x + 3)}{8 x}$

Step 5.2

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

$\frac{2 \cdot x - 5 \cdot 2 - (x + 3)}{8 x}$

Step 5.3

Multiply $- 5$ by $2$ .

$\frac{2 \cdot x - 10 - (x + 3)}{8 x}$

Step 5.4

Apply the distributive property.

$\frac{2 x - 10 - x - 1 \cdot 3}{8 x}$

Step 5.5

Multiply $- 1$ by $3$ .

$\frac{2 x - 10 - x - 3}{8 x}$

Step 5.6

Subtract $x$ from $2 x$ .

$\frac{x - 10 - 3}{8 x}$

Step 5.7

Subtract $3$ from $- 10$ .

$\frac{x - 13}{8 x}$