What is 1/(x^2+2x-24)+2/(x^2-2x-8)-3/(x^2+8x+12) ?

The solution to 1/(x^2+2x-24)+2/(x^2-2x-8)-3/(x^2+8x+12) is (26)/((x-4)(x+6)(x+2))

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simplify 1/(x^2+2x-24)+2/(x^2-2x-8)-3/(x^2+8x+12)

simplify

\frac{1}{x ^{2} + 2 x - 24} + \frac{2}{x ^{2} - 2 x - 8} - \frac{3}{x ^{2} + 8 x + 12}

\frac{26}{( x - 4 ) ( x + 6 ) ( x + 2 )}

Solution steps

\frac{1}{x ^{2} + 2 x - 24} + \frac{2}{x ^{2} - 2 x - 8} - \frac{3}{x ^{2} + 8 x + 12}

Least Common Multiplier of

x^{2} + 2 x - 24, x^{2} - 2 x - 8, x^{2} + 8 x + 12 : (x - 4) (x + 6) (x + 2)

Adjust Fractions based on the LCM

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

Apply the fraction rule:

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

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

Simplify

x + 2 + 2 (x + 6) - 3 (x - 4) : 26

= \frac{26}{( x - 4 ) ( x + 6 ) ( x + 2 )}

50 \div 10

\frac{2}{40}

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

\frac{1}{6} - \frac{1}{9}

y^{2} + 3 y + 2

What is 1/(x^2+2x-24)+2/(x^2-2x-8)-3/(x^2+8x+12) ?
The solution to 1/(x^2+2x-24)+2/(x^2-2x-8)-3/(x^2+8x+12) is (26)/((x-4)(x+6)(x+2))