multiplying complex fractions

Question

xy+xc+ay+ac                  2x to third power - 8x

___________        X       ___________________

 

xy-2xc+ay-2ac                12x to third power + 20x - 8x

 

 

How do I solve this?

Answer 1

E = ((xy+xc+ay+ac)/(xy-2xc+ay-2ac))
*(2x^3-8x)/(12x^3+20x-8x)

E = ((x(y+c)+a(y+c))/(x(y-2c)+a(y-2c)))
*(2x(x^2-4))/(12x^3+12x)

E = (((y+c)(x+a))/((y-2c)(x+a)))
*(2x(x+2)(x-2))/(12x(x^2+1))

E = ((x+a)/(x+a))*((y+c)/(y-2c))
*((2x)/(2x))*((x+2)(x-2))/(6(x^2+1))

(x+a)/(x+a) = {UNDEFINED if x=–a, 1 if x≠-a}
(2x)/(2x) = {UNDEFINED if x=0, 1 if x≠0}

These are called “Holes”.

E = ((y+c)/(y-2c))*((x+2)(x-2))/(6(x^2+1)), x≠{-a,0}

E = (x+2)(x-2)(y+c)/(6(x^2+1)(y-2c)), x≠{-a,0}