What is 2/(x-2)+x/(x+9)-(x+20)/(x^2+7x-18) ?

The solution to 2/(x-2)+x/(x+9)-(x+20)/(x^2+7x-18) is (x+1)/(x+9)

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simplify 2/(x-2)+x/(x+9)-(x+20)/(x^2+7x-18)

simplify

\frac{2}{x - 2} + \frac{x}{x + 9} - \frac{x + 20}{x ^{2} + 7 x - 18}

\frac{x + 1}{x + 9}

Solution steps

\frac{2}{x - 2} + \frac{x}{x + 9} - \frac{x + 20}{x ^{2} + 7 x - 18}

Least Common Multiplier of

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

Adjust Fractions based on the LCM

= \frac{2 ( x + 9 )}{( x - 2 ) ( x + 9 )} + \frac{x ( x - 2 )}{( x - 2 ) ( x + 9 )} - \frac{x + 20}{( x - 2 ) ( x + 9 )}

Apply the fraction rule:

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

= \frac{2 ( x + 9 ) + x ( x - 2 ) - ( x + 20 )}{( x - 2 ) ( x + 9 )}

Simplify

2 (x + 9) + x (x - 2) - (x + 20) : x^{2} - x - 2

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

Cancel

\frac{x ^{2} - x - 2}{( x - 2 ) ( x + 9 )} : \frac{x + 1}{x + 9}

= \frac{x + 1}{x + 9}

- 2 x + 6 x - 11 x

245 a b^{5}

\frac{5 !}{( 5 - 4 ) !}

lo g_{3} (\frac{1}{16})

\frac{x - 1}{3} - \frac{x - 2}{4} - \frac{x + 3}{6}

What is 2/(x-2)+x/(x+9)-(x+20)/(x^2+7x-18) ?
The solution to 2/(x-2)+x/(x+9)-(x+20)/(x^2+7x-18) is (x+1)/(x+9)