What is x/(x^2-x-2)-x/(x^2+4x-12)-2/(x^2+7x+6) ?

The solution to x/(x^2-x-2)-x/(x^2+4x-12)-2/(x^2+7x+6) is (3x+4)/((x+1)(x-2)(x+6))

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simplify x/(x^2-x-2)-x/(x^2+4x-12)-2/(x^2+7x+6)

simplify

\frac{x}{x ^{2} - x - 2} - \frac{x}{x ^{2} + 4 x - 12} - \frac{2}{x ^{2} + 7 x + 6}

\frac{3 x + 4}{( x + 1 ) ( x - 2 ) ( x + 6 )}

Solution steps

\frac{x}{x ^{2} - x - 2} - \frac{x}{x ^{2} + 4 x - 12} - \frac{2}{x ^{2} + 7 x + 6}

Least Common Multiplier of

x^{2} - x - 2, x^{2} + 4 x - 12, x^{2} + 7 x + 6 : (x + 1) (x - 2) (x + 6)

Adjust Fractions based on the LCM

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

Apply the fraction rule:

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

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

Simplify

x (x + 6) - x (x + 1) - 2 (x - 2) : 3 x + 4

= \frac{3 x + 4}{( x + 1 ) ( x - 2 ) ( x + 6 )}

\frac{12 b}{6}

1 - 2 sin^{2} (x) + sin^{4} (x)

\frac{1}{4} 4^{44}

27 p^{3} - 8 q^{3}

\frac{x ^{2} - 4}{x ^{2} - x - 6}

What is x/(x^2-x-2)-x/(x^2+4x-12)-2/(x^2+7x+6) ?
The solution to x/(x^2-x-2)-x/(x^2+4x-12)-2/(x^2+7x+6) is (3x+4)/((x+1)(x-2)(x+6))