(x+2)/(x-3) - (x-1)/(x+3) can be written in the form (ax+b)/(x^2-9). Work out the value of a and the value of b.

Recall that in order to add and subtract fractions, they must have the same denominator. Therefore, we multiply the first fraction by (x+3)/(x+3) and the second fraction by (x-3)/(x-3) to create a common denominator of (x-3)(x+3) (which is equivalent to x²-9). The next step is to expand out and simplify the numerator;(x+2)(x+3) - (x-1)(x-3) = x²+2x+3x+6 -(x²-x-3x+3) = x²+5x+6 -(x²-4x+3) = x²+5x+6-x²+4x-3=9x+3. This leaves us with the fraction as (9x+3)/(x²-9). Our final step is to identify a and b. We can see that a=9 and b=3.