complex fraction subtraction

Question

Please help me

 

       6                                  9

___________    ___      ___________

 

X squared - 9                X squared -6x + 9

 

I can factor X squared and the X squared minus -6 + 9 to

 

 

(X-3) (X+3)   and (X - 3) ( x - 3)   but I am lost on how to perform the rest of the problem. 

 

Thank you

Answer 1

f(x) = 6/(x^2-9) – 9/(x^2–6x+9)

f(x) = 6/((x-3)(x+3)) – 9/((x–3)(x–3))

As in all fraction addition/subtraction problems, we need the same denominator before we can subtract:

f(x) = 6(x-3)/((x-3)(x-3)(x+3))

– 9(x+3)/((x–3)(x–3)(x+3))

f(x) = (6(x-3) – 9(x+3))/((x–3)(x–3)(x+3))

f(x) = (6x-18 – 9x-27))/((x–3)(x–3)(x+3))

f(x) = (-3x-45))/((x–3)(x–3)(x+3))

f(x) = -3(x+15))/((x+3)(x–3)^2)