What is (x+2)/(x^2-3x-18)-(5x)/(x-6) ?

The solution to (x+2)/(x^2-3x-18)-(5x)/(x-6) is (-5x^2-14x+2)/((x+3)(x-6))

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simplify (x+2)/(x^2-3x-18)-(5x)/(x-6)

simplify

\frac{x + 2}{x ^{2} - 3 x - 18} - \frac{5 x}{x - 6}

\frac{- 5 x ^{2} - 14 x + 2}{( x + 3 ) ( x - 6 )}

Solution steps

\frac{x + 2}{x ^{2} - 3 x - 18} - \frac{5 x}{x - 6}

Least Common Multiplier of

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

Adjust Fractions based on the LCM

= \frac{x + 2}{( x + 3 ) ( x - 6 )} - \frac{5 x ( x + 3 )}{( x + 3 ) ( x - 6 )}

Apply the fraction rule:

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

= \frac{x + 2 - 5 x ( x + 3 )}{( x + 3 ) ( x - 6 )}

Simplify

x + 2 - 5 x (x + 3) : - 5 x^{2} - 14 x + 2

= \frac{- 5 x ^{2} - 14 x + 2}{( x + 3 ) ( x - 6 )}

lo g_{0} (x)

(4 - 5 i) (- 1 - 7 i)

\frac{23}{6}

(s + 4)^{2}

What is (x+2)/(x^2-3x-18)-(5x)/(x-6) ?
The solution to (x+2)/(x^2-3x-18)-(5x)/(x-6) is (-5x^2-14x+2)/((x+3)(x-6))