Simplify (3x+2)/(x+6)-x

$\frac{3 x + 2}{x + 6} - x$

Step 1

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

$\frac{3 x + 2}{x + 6} - x \cdot \frac{x + 6}{x + 6}$

Step 2

Simplify terms.

Combine $- x$ and $\frac{x + 6}{x + 6}$ .

$\frac{3 x + 2}{x + 6} + \frac{- x (x + 6)}{x + 6}$

Combine the numerators over the common denominator.

$\frac{3 x + 2 - x (x + 6)}{x + 6}$

Step 3

Simplify the numerator.

Apply the distributive property.

$\frac{3 x + 2 - x \cdot x - x \cdot 6}{x + 6}$

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

Move $x$ .

$\frac{3 x + 2 - (x \cdot x) - x \cdot 6}{x + 6}$

Multiply $x$ by $x$ .

$\frac{3 x + 2 - x^{2} - x \cdot 6}{x + 6}$

Multiply $6$ by $- 1$ .

$\frac{3 x + 2 - x^{2} - 6 x}{x + 6}$

Subtract $6 x$ from $3 x$ .

$\frac{- 3 x + 2 - x^{2}}{x + 6}$

Reorder terms.

$\frac{- x^{2} - 3 x + 2}{x + 6}$

Step 4

Simplify with factoring out.

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

$\frac{- (x^{2}) - 3 x + 2}{x + 6}$

Factor $- 1$ out of $- 3 x$ .

$\frac{- (x^{2}) - (3 x) + 2}{x + 6}$

Factor $- 1$ out of $- (x^{2}) - (3 x)$ .

$\frac{- (x^{2} + 3 x) + 2}{x + 6}$

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

$\frac{- (x^{2} + 3 x) - 1 (- 2)}{x + 6}$

Factor $- 1$ out of $- (x^{2} + 3 x) - 1 (- 2)$ .

$\frac{- (x^{2} + 3 x - 2)}{x + 6}$

Simplify the expression.

Rewrite $- (x^{2} + 3 x - 2)$ as $- 1 (x^{2} + 3 x - 2)$ .

$\frac{- 1 (x^{2} + 3 x - 2)}{x + 6}$

Move the negative in front of the fraction.

$- \frac{x^{2} + 3 x - 2}{x + 6}$