What is (x^2-x+9)/(x^3-9x)+1/(x^2-9)-1/(x-3)+1/x ?

The solution to (x^2-x+9)/(x^3-9x)+1/(x^2-9)-1/(x-3)+1/x is 1/(x+3)

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simplify (x^2-x+9)/(x^3-9x)+1/(x^2-9)-1/(x-3)+1/x

simplify

\frac{x ^{2} - x + 9}{x ^{3} - 9 x} + \frac{1}{x ^{2} - 9} - \frac{1}{x - 3} + \frac{1}{x}

\frac{1}{x + 3}

Solution steps

\frac{x ^{2} - x + 9}{x ^{3} - 9 x} + \frac{1}{x ^{2} - 9} - \frac{1}{x - 3} + \frac{1}{x}

Least Common Multiplier of

x^{3} - 9 x, x^{2} - 9, x - 3, x : x (x + 3) (x - 3)

Adjust Fractions based on the LCM

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

Apply the fraction rule:

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

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

Simplify

x^{2} - x + 9 + x - x (x + 3) + (x + 3) (x - 3) : x^{2} - x (x + 3) + (x + 3) (x - 3) + 9

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

Simplify

x^{2} - x (x + 3) + (x + 3) (x - 3) + 9 : x^{2} - 3 x

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

Cancel

\frac{x ^{2} - 3 x}{x ( x + 3 ) ( x - 3 )} : \frac{1}{x + 3}

= \frac{1}{x + 3}

36 r^{2} s + 48 r s^{2} + 16 s^{3}

- 8 + (- 8)

\frac{8 x}{x ^{2} - 49} + \frac{5}{x ^{2} - 4 x - 21}

- 9 - - 2 - 121 - - 2

What is (x^2-x+9)/(x^3-9x)+1/(x^2-9)-1/(x-3)+1/x ?
The solution to (x^2-x+9)/(x^3-9x)+1/(x^2-9)-1/(x-3)+1/x is 1/(x+3)