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

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

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

simplify

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

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

Solution steps

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

Least Common Multiplier of

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

Adjust Fractions based on the LCM

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

Apply the fraction rule:

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

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

Simplify

(x - 9) x + (x + 9) (x - 3) + (x + 3)^{2} : 3 x^{2} + 3 x - 18

= \frac{3 x ^{2} + 3 x - 18}{x ( x + 3 ) ( x - 3 )}

Cancel

\frac{3 x ^{2} + 3 x - 18}{x ( x + 3 ) ( x - 3 )} : \frac{3 ( x - 2 )}{x ( x - 3 )}

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

15 x^{3} y^{2} + 10 x^{2} y^{3} - 15 x^{2} y^{2} z

(2 x + 2) (x - 1)

\frac{cos ( θ )}{sec ( θ )} + \frac{sin ( θ )}{csc ( θ )}

\frac{49}{36}

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

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