How do you divide #(5x^2+12x-9) /(x^2+3x-10)#?
Before attempting long division or synthetic division, try factoring first
We cannot cancel anything because there are 3 terms on the top and 3 terms on the bottom. We can only cancel if we have factors.
Factorise the numerator and the denominator. Both are quadratic trinomials.
Oops, there are no factors which can cancel. so we will have to try one of the other methods.
Long division gives the result: