What is x/(x^2+x-2)-3/(x^2+2x-3)-x/(x^2+5x+6) ?

The solution to x/(x^2+x-2)-3/(x^2+2x-3)-x/(x^2+5x+6) is (x-6)/((x-1)(x+2)(x+3))

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simplify x/(x^2+x-2)-3/(x^2+2x-3)-x/(x^2+5x+6)

simplify

\frac{x}{x ^{2} + x - 2} - \frac{3}{x ^{2} + 2 x - 3} - \frac{x}{x ^{2} + 5 x + 6}

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

Solution steps

\frac{x}{x ^{2} + x - 2} - \frac{3}{x ^{2} + 2 x - 3} - \frac{x}{x ^{2} + 5 x + 6}

Least Common Multiplier of

x^{2} + x - 2, x^{2} + 2 x - 3, x^{2} + 5 x + 6 : (x - 1) (x + 2) (x + 3)

Adjust Fractions based on the LCM

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

Apply the fraction rule:

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

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

Simplify

x (x + 3) - 3 (x + 2) - x (x - 1) : x - 6

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

- 4^{1}

\frac{3}{2} x

y^{2} + 4 y

\frac{3}{4} + \frac{2}{5} - \frac{1}{6} + \frac{1}{12}

\frac{1}{2} - 16

What is x/(x^2+x-2)-3/(x^2+2x-3)-x/(x^2+5x+6) ?
The solution to x/(x^2+x-2)-3/(x^2+2x-3)-x/(x^2+5x+6) is (x-6)/((x-1)(x+2)(x+3))