Question

x^2-x-12/x^2-3x-4*x^2-1/x^2+2x-3

Please help me solve, I am desperate!

Answer 1

When simplifying rational expressions you need to factor all the numerators & denominators (if possible):
x^2-x-12 --> (x-4)(x+3)
x^2-3x-4 --> (x-4)(x+1)

x^2-1 -----> (x+1)(x-1)
x^2+2x-3 --> (x+3)(x-1)

Therefore you will have:
(x-4)(x+3)*(x+1)(x-1)
(x-4)(x+1) (x+3)(x-1)

You can then cancel out all common factors that appear on top and bottom. If you notice, for every factor on top, there is a match on the bottom. THus, everything cancels out leaving you with a final answer of 1!