Combine The Rational Expressions and Simplify (3x-7)/(x^2-12x+27)-(3x-8)/(x^2-9x+18)+(x+2)/(x^2-15x+54)
factor first
(3x-2)/((x-3)(x-9)) - (3x-8)/((x-3)(x-6)) + (x+2)/((x-9)(x-6))
so the LCD is ((x-3)(x-6)(x-9)
= [ (3x-2)(x-6) - (3x-8)(x-9) + (x+2)(x-3) ]/[(x-3)(x-6)(x-9)]
= [3x^2 - 20x + 12 - 3x^2 + 35x - 72 + x^2 - x - 6]/[(x-3)(x-6)(x-9)]
= (x^2 + 14x -66)/[(x-3)(x-6)(x-9)]
check my arithmetic