What is 3/((x^2+3x))-1/x-6/((x^2-9)) ?

The solution to 3/((x^2+3x))-1/x-6/((x^2-9)) is -1/(x-3)

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simplify 3/((x^2+3x))-1/x-6/((x^2-9))

simplify

\frac{3}{( x ^{2} + 3 x )} - \frac{1}{x} - \frac{6}{( x ^{2} - 9 )}

- \frac{1}{x - 3}

Solution steps

\frac{3}{x ^{2} + 3 x} - \frac{1}{x} - \frac{6}{x ^{2} - 9}

Least Common Multiplier of

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

Adjust Fractions based on the LCM

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

Apply the fraction rule:

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

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

Simplify

3 (x - 3) - (x + 3) (x - 3) - 6 x : - 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}

50 a^{2} + 75 a^{2} \cdot b

x^{4} y - x y^{4}

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

2 x^{3} - 2 x^{2} - 8 x

(3 x^{- 4})^{2}

What is 3/((x^2+3x))-1/x-6/((x^2-9)) ?
The solution to 3/((x^2+3x))-1/x-6/((x^2-9)) is -1/(x-3)