What is 3/(x+6)+2/(x-2)+(x+30)/(x^2+4x-12) ?

The solution to 3/(x+6)+2/(x-2)+(x+30)/(x^2+4x-12) is 6/(x-2)

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simplify 3/(x+6)+2/(x-2)+(x+30)/(x^2+4x-12)

simplify

\frac{3}{x + 6} + \frac{2}{x - 2} + \frac{x + 30}{x ^{2} + 4 x - 12}

\frac{6}{x - 2}

Solution steps

\frac{3}{x + 6} + \frac{2}{x - 2} + \frac{x + 30}{x ^{2} + 4 x - 12}

Least Common Multiplier of

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

Adjust Fractions based on the LCM

= \frac{3 ( x - 2 )}{( x + 6 ) ( x - 2 )} + \frac{2 ( x + 6 )}{( x + 6 ) ( x - 2 )} + \frac{x + 30}{( x + 6 ) ( x - 2 )}

Apply the fraction rule:

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

= \frac{3 ( x - 2 ) + 2 ( x + 6 ) + x + 30}{( x + 6 ) ( x - 2 )}

Simplify

3 (x - 2) + 2 (x + 6) + x + 30 : 6 x + 36

= \frac{6 x + 36}{( x + 6 ) ( x - 2 )}

Cancel

\frac{6 x + 36}{( x + 6 ) ( x - 2 )} : \frac{6}{x - 2}

= \frac{6}{x - 2}

\frac{\frac{m}{m}}{s t}

- 6 x^{- 2}

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

220 + 345

(a^{2} + b^{2})^{3}

What is 3/(x+6)+2/(x-2)+(x+30)/(x^2+4x-12) ?
The solution to 3/(x+6)+2/(x-2)+(x+30)/(x^2+4x-12) is 6/(x-2)