Question 88539
*[Tex \LARGE \frac{6x^2 + 6x + 42}{(x+5)(x+2)(x-4)} - \frac{6}{x + 5}] 



*[Tex \LARGE \frac{6x^2 + 6x + 42}{(x+5)(x+2)(x-4)} - \left(\frac{(x+2)(x-4)}{(x+2)(x-4)}\right)\left(\frac{6}{x + 5}\right)] Multiply the second fraction by *[Tex \Large \frac{(x+2)(x-4)}{(x+2)(x-4)}]


*[Tex \LARGE \frac{6x^2 + 6x + 42}{(x+5)(x+2)(x-4)} - \left(\frac{6(x+2)(x-4)}{(x+5)(x+2)(x-4)}\right)] 



*[Tex \LARGE \frac{6x^2 + 6x + 42}{(x+5)(x+2)(x-4)} - \left(\frac{6(x^2-2x-8)}{(x+5)(x+2)(x-4)}\right)] Foil


*[Tex \LARGE \frac{6x^2 + 6x + 42}{(x+5)(x+2)(x-4)} - \left(\frac{6x^2-12x-48}{(x+5)(x+2)(x-4)}\right)] Distribute


*[Tex \LARGE \frac{(6x^2 + 6x + 42)-(6x^2-12x-48)}{(x+5)(x+2)(x-4)}] Combine the fractions


*[Tex \LARGE \frac{6x^2 + 6x + 42-6x^2+12x+48}{(x+5)(x+2)(x-4)}] Distribute the negative


*[Tex \LARGE \frac{18x+90}{(x+5)(x+2)(x-4)}] Combine like terms


*[Tex \LARGE \frac{18(x+5)}{(x+5)(x+2)(x-4)}] Factor out an 18


*[Tex \LARGE \frac{18}{(x+2)(x-4)}] Reduce


*[Tex \LARGE \frac{18}{x^2-2x-8}] Foil the denominator


So 


*[Tex \LARGE \frac{6x^2 + 6x + 42}{(x+5)(x+2)(x-4)} - \frac{6}{x + 5}]  


simplifies to


*[Tex \LARGE \frac{18}{x^2-2x-8}]



As always, you can verify by graphing the original and the simplified expressions to compare them