Question

7-5). Reduce the following rational expression to lowest terms, if possible.
2x^2+5x-12
____________
x^4-256

Answer 1

Try to factorise top and bottom.

Top factorises as (2x - 3)(x + 4). Do you know how to factorise a non-monic quadratic expression?

The bottom looks like the difference of two squares: x^2 squared and 16 squared

So bottom is (x^2 +16)(x^2 - 16), but second bracket is again the difference between two squares

So bottom line is (x^2 + 16)(x - 4)(x + 4)

We can cancel top and bottom (x + 4) to give us:

(2x - 3)/(x^2 + 16)(x - 4)