Simplify 2/(x-4)-7x

$\frac{2}{x - 4} - 7 x$

To write $- 7 x$ as a fraction with a common denominator, multiply by $\frac{x - 4}{x - 4}$ .

$\frac{2}{x - 4} - 7 x \cdot \frac{x - 4}{x - 4}$

Simplify terms.

Combine $- 7 x$ and $\frac{x - 4}{x - 4}$ .

$\frac{2}{x - 4} + \frac{- 7 x (x - 4)}{x - 4}$

Combine the numerators over the common denominator.

$\frac{2 - 7 x (x - 4)}{x - 4}$

Simplify the numerator.

Apply the distributive property.

$\frac{2 - 7 x \cdot x - 7 x \cdot - 4}{x - 4}$

Multiply $x$ by $x$ by adding the exponents.

Move $x$ .

$\frac{2 - 7 (x \cdot x) - 7 x \cdot - 4}{x - 4}$

Multiply $x$ by $x$ .

$\frac{2 - 7 x^{2} - 7 x \cdot - 4}{x - 4}$

Multiply $- 4$ by $- 7$ .

$\frac{2 - 7 x^{2} + 28 x}{x - 4}$

Reorder terms.

$\frac{- 7 x^{2} + 28 x + 2}{x - 4}$

Simplify with factoring out.

Factor $- 1$ out of $- 7 x^{2}$ .

$\frac{- (7 x^{2}) + 28 x + 2}{x - 4}$

Factor $- 1$ out of $28 x$ .

$\frac{- (7 x^{2}) - (- 28 x) + 2}{x - 4}$

Factor $- 1$ out of $- (7 x^{2}) - (- 28 x)$ .

$\frac{- (7 x^{2} - 28 x) + 2}{x - 4}$

Rewrite $2$ as $- 1 (- 2)$ .

$\frac{- (7 x^{2} - 28 x) - 1 (- 2)}{x - 4}$

Factor $- 1$ out of $- (7 x^{2} - 28 x) - 1 (- 2)$ .

$\frac{- (7 x^{2} - 28 x - 2)}{x - 4}$

Simplify the expression.

Rewrite $- (7 x^{2} - 28 x - 2)$ as $- 1 (7 x^{2} - 28 x - 2)$ .

$\frac{- 1 (7 x^{2} - 28 x - 2)}{x - 4}$

Move the negative in front of the fraction.

$- \frac{7 x^{2} - 28 x - 2}{x - 4}$