Adding Unlike Denominators

Question

    1                2

__________ + ___________     Factor each denominator completely.

x^2 -3x -4       x^2 -1

   1            2

_________ + ____________      Find the common denominator, which is the product of

(x-4)(x+1)     (x+1)(x-1)         each prime factor the number of times it is a factor in

                             any one denominator. WHAAT?

Can someone please explain that last instruction much simpler than my text book is offering. And also provide a solution.

Thank You,

Brian

Answer 1

1/(x-4)(x+1) + 2/(x-1)(x+1)

= (x-1 + 2x-8)//(x-4(x+1)(x-1)

= (3x -9)/(x-4)(x^2-1)

= (3x -9)/(x^3 -4x^2 -x +4)

think of a = x-4, b = x-1, c = x+1

then LCD = Least Common Denominator = abc

and 1/ab + 2/bc = c/abc + 2a/abc = (c+2a)/abc