What is 1/(x-6)-(3x)/(x^2-3x-18) ?

The solution to 1/(x-6)-(3x)/(x^2-3x-18) is (-2x+3)/((x-6)(x+3))

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

simplify

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

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

Solution steps

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

Least Common Multiplier of

x - 6, x^{2} - 3 x - 18 : (x - 6) (x + 3)

Adjust Fractions based on the LCM

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

Apply the fraction rule:

\frac{a}{c} - \frac{b}{c} = \frac{a - b}{c}

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

Simplify

x + 3 - 3 x : - 2 x + 3

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

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

\frac{25}{40}

(- 8 a + 9 b)^{2}

(4 a^{3} - 3 a - 8) - (a - 5)

- 2^{8}

What is 1/(x-6)-(3x)/(x^2-3x-18) ?
The solution to 1/(x-6)-(3x)/(x^2-3x-18) is (-2x+3)/((x-6)(x+3))