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

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

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

simplify

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

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

Solution steps

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

Least Common Multiplier of

x, x^{2} + x, x + 3 : x (x + 1) (x + 3)

Adjust Fractions based on the LCM

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

Apply the fraction rule:

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

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

Simplify

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

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

\frac{( 2 - i ) ^{2} - i ^{15}}{3 + i}

(\frac{9 x ^{2}}{4 y ^{3}}) (\frac{2 y ^{2}}{x})

\frac{cot ( x )}{cos ( x )}

9 (x - 1) - (x - 1)^{2}

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