Question 88520
*[Tex \LARGE \frac{3x^2-26x+80}{(x-6)(x-4)(x+2)} - \frac{3}{x + 2}] 



*[Tex \LARGE \frac{3x^2-26x+80}{(x-6)(x-4)(x+2)} - \left(\frac{(x-6)(x-4)}{(x-6)(x-4)}\right)\left(\frac{3}{x + 2}\right)] Multiply the second fraction by *[Tex \Large \frac{(x-6)(x-4)}{(x-6)(x-4)}]


*[Tex \LARGE \frac{3x^2-26x+80}{(x-6)(x-4)(x+2)} - \left(\frac{3(x-6)(x-4)}{(x-6)(x-4)(x + 2)}\right)] 



*[Tex \LARGE \frac{3x^2-26x+80}{(x-6)(x-4)(x+2)} - \left(\frac{3(x^2-10x+24)}{(x-6)(x-4)(x + 2)}\right)] Foil


*[Tex \LARGE \frac{3x^2-26x+80}{(x-6)(x-4)(x+2)} - \left(\frac{3x^2-30x+72}{(x-6)(x-4)(x + 2)}\right)] Distribute


*[Tex \LARGE \frac{(3x^2-26x+80)-(3x^2-30x+72)}{(x-6)(x-4)(x+2)}] Combine the fractions


*[Tex \LARGE \frac{3x^2-26x+80-3x^2+30x-72}{(x-6)(x-4)(x+2)}] Distribute the negative


*[Tex \LARGE \frac{4x+8}{(x-6)(x-4)(x+2)}] Combine like terms


*[Tex \LARGE \frac{4(x+2)}{(x-6)(x-4)(x+2)}] Factor out a 4


*[Tex \LARGE \frac{4}{(x-6)(x-4)}] Reduce


*[Tex \LARGE \frac{4}{x^2-10x+24}] Foil the denominator


So 


*[Tex \LARGE \frac{3x^2-26x+80}{(x-6)(x-4)(x+2)} - \frac{3}{x + 2}] 


simplifies to


*[Tex \LARGE \frac{4}{x^2-10x+24}]



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