What is the sum of 3 over x-3 and x over 3-x?

Answer 1

First, give them a common denominator by multiplying (x-3) and (3-x), which gives you -1(x-3)^2.

Then, you have to multiply the first 3 of the numerator with (3-x) and x with (x-3). This will give you x^2-6x+9 over -(x-3)^2, which will simplify to (x-3)^2 over -(x-3)^2.

The top and the bottom of the fraction will simplify and give you 1 over -1, which is simply:

-1.