Simplify 1/(x+3)-5x

$\frac{1}{x + 3} - 5 x$

Step 1

To write $- 5 x$ as a fraction with a common denominator, multiply by $\frac{x + 3}{x + 3}$ .

$\frac{1}{x + 3} - 5 x \cdot \frac{x + 3}{x + 3}$

Step 2

Simplify terms.

Combine $- 5 x$ and $\frac{x + 3}{x + 3}$ .

$\frac{1}{x + 3} + \frac{- 5 x (x + 3)}{x + 3}$

Combine the numerators over the common denominator.

$\frac{1 - 5 x (x + 3)}{x + 3}$

Step 3

Simplify the numerator.

Apply the distributive property.

$\frac{1 - 5 x \cdot x - 5 x \cdot 3}{x + 3}$

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

Move $x$ .

$\frac{1 - 5 (x \cdot x) - 5 x \cdot 3}{x + 3}$

Multiply $x$ by $x$ .

$\frac{1 - 5 x^{2} - 5 x \cdot 3}{x + 3}$

Multiply $3$ by $- 5$ .

$\frac{1 - 5 x^{2} - 15 x}{x + 3}$

Reorder terms.

$\frac{- 5 x^{2} - 15 x + 1}{x + 3}$

Step 4

Simplify with factoring out.

Factor $- 1$ out of $- 5 x^{2}$ .

$\frac{- (5 x^{2}) - 15 x + 1}{x + 3}$

Factor $- 1$ out of $- 15 x$ .

$\frac{- (5 x^{2}) - (15 x) + 1}{x + 3}$

Factor $- 1$ out of $- (5 x^{2}) - (15 x)$ .

$\frac{- (5 x^{2} + 15 x) + 1}{x + 3}$

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

$\frac{- (5 x^{2} + 15 x) - 1 (- 1)}{x + 3}$

Factor $- 1$ out of $- (5 x^{2} + 15 x) - 1 (- 1)$ .

$\frac{- (5 x^{2} + 15 x - 1)}{x + 3}$

Simplify the expression.

Rewrite $- (5 x^{2} + 15 x - 1)$ as $- 1 (5 x^{2} + 15 x - 1)$ .

$\frac{- 1 (5 x^{2} + 15 x - 1)}{x + 3}$

Move the negative in front of the fraction.

$- \frac{5 x^{2} + 15 x - 1}{x + 3}$