Simplify (x-4)/(5x)-12/(5(x-4))

$\frac{x - 4}{5 x} - \frac{12}{5 (x - 4)}$

Step 1

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

$\frac{x - 4}{5 x} \cdot \frac{x - 4}{x - 4} - \frac{12}{5 (x - 4)}$

Step 2

To write $- \frac{12}{5 (x - 4)}$ as a fraction with a common denominator, multiply by $\frac{x}{x}$ .

$\frac{x - 4}{5 x} \cdot \frac{x - 4}{x - 4} - \frac{12}{5 (x - 4)} \cdot \frac{x}{x}$

Step 3

Write each expression with a common denominator of $5 x (x - 4)$ , by multiplying each by an appropriate factor of $1$ .

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

$\frac{(x - 4) (x - 4)}{5 x (x - 4)} - \frac{12}{5 (x - 4)} \cdot \frac{x}{x}$

Multiply $\frac{12}{5 (x - 4)}$ by $\frac{x}{x}$ .

$\frac{(x - 4) (x - 4)}{5 x (x - 4)} - \frac{12 x}{5 (x - 4) x}$

Reorder the factors of $5 (x - 4) x$ .

$\frac{(x - 4) (x - 4)}{5 x (x - 4)} - \frac{12 x}{5 x (x - 4)}$

Step 4

Combine the numerators over the common denominator.

$\frac{(x - 4) (x - 4) - 12 x}{5 x (x - 4)}$

Step 5

Simplify the numerator.

Expand $(x - 4) (x - 4)$ using the FOIL Method.

Apply the distributive property.

$\frac{x (x - 4) - 4 (x - 4) - 12 x}{5 x (x - 4)}$

Apply the distributive property.

$\frac{x \cdot x + x \cdot - 4 - 4 (x - 4) - 12 x}{5 x (x - 4)}$

Apply the distributive property.

$\frac{x \cdot x + x \cdot - 4 - 4 x - 4 \cdot - 4 - 12 x}{5 x (x - 4)}$

Simplify and combine like terms.

Simplify each term.

Multiply $x$ by $x$ .

$\frac{x^{2} + x \cdot - 4 - 4 x - 4 \cdot - 4 - 12 x}{5 x (x - 4)}$

Move $- 4$ to the left of $x$ .

$\frac{x^{2} - 4 \cdot x - 4 x - 4 \cdot - 4 - 12 x}{5 x (x - 4)}$

Multiply $- 4$ by $- 4$ .

$\frac{x^{2} - 4 x - 4 x + 16 - 12 x}{5 x (x - 4)}$

Subtract $4 x$ from $- 4 x$ .

$\frac{x^{2} - 8 x + 16 - 12 x}{5 x (x - 4)}$

Subtract $12 x$ from $- 8 x$ .

$\frac{x^{2} - 20 x + 16}{5 x (x - 4)}$