What is (x+6)/(x^2-7x-18)-(2x)/(x-9) ?

The solution to (x+6)/(x^2-7x-18)-(2x)/(x-9) is (-2x^2-3x+6)/((x+2)(x-9))

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simplify (x+6)/(x^2-7x-18)-(2x)/(x-9)

simplify

\frac{x + 6}{x ^{2} - 7 x - 18} - \frac{2 x}{x - 9}

\frac{- 2 x ^{2} - 3 x + 6}{( x + 2 ) ( x - 9 )}

Solution steps

\frac{x + 6}{x ^{2} - 7 x - 18} - \frac{2 x}{x - 9}

Least Common Multiplier of

x^{2} - 7 x - 18, x - 9 : (x + 2) (x - 9)

Adjust Fractions based on the LCM

= \frac{x + 6}{( x + 2 ) ( x - 9 )} - \frac{2 x ( x + 2 )}{( x + 2 ) ( x - 9 )}

Apply the fraction rule:

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

= \frac{x + 6 - 2 x ( x + 2 )}{( x + 2 ) ( x - 9 )}

Simplify

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

= \frac{- 2 x ^{2} - 3 x + 6}{( x + 2 ) ( x - 9 )}

- x - x

15 - 5

\frac{x ^{2} - \frac{1}{x}}{1 - \frac{1}{x}}

\frac{7 + 5}{7 - 5}

3 (0)

What is (x+6)/(x^2-7x-18)-(2x)/(x-9) ?
The solution to (x+6)/(x^2-7x-18)-(2x)/(x-9) is (-2x^2-3x+6)/((x+2)(x-9))