Simplify 1/(x-6)-(3x)/(x^2-3x-18)

$\frac{1}{x - 6} - \frac{3 x}{x^{2} - 3 x - 18}$

Factor $x^{2} - 3 x - 18$ using the AC method.

Consider the form $x^{2} + b x + c$ . Find a pair of integers whose product is $c$ and whose sum is $b$ . In this case, whose product is $- 18$ and whose sum is $- 3$ .

$- 6, 3$

Write the factored form using these integers.

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

To write $\frac{1}{x - 6}$ as a fraction with a common denominator, multiply by $\frac{x + 3}{x + 3}$ .

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

Multiply $\frac{1}{x - 6}$ by $\frac{x + 3}{x + 3}$ .

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

Combine the numerators over the common denominator.

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

Subtract $3 x$ from $x$ .

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

Factor $- 1$ out of $- 2 x$ .

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

Rewrite $3$ as $- 1 (- 3)$ .

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

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

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

Simplify the expression.

Rewrite $- (2 x - 3)$ as $- 1 (2 x - 3)$ .

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

Move the negative in front of the fraction.

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

Simplify 1/(x-6)-(3x)/(x^2-3x-18)

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