In other words, my text book says:

b - c = -(c - b)

That seems obvious enough.

It also says:

a / b + c / d = ad + bc / bd

That seems clear too. It then goes onto say:

(x-a)(x-b) / (c-a)(c-b) + (x-a)(x-c) / (b-a)(b-c)

= (x-a)(x-b)(b-a) - (x-a)(x-c)(c-a) / (c-a)(c-b)(b-a)

There are 2 things I don't understand about this. One is that the first expression is adding fractions and yet in the second it is subtracting them. I don't see how it turned into a subtraction.

The second thing I don't understand is how it got the denominator (c-a)(c-b)(b-a) from (c-a)(c-b) and (b-a)(b-c).