Simplify the algebraic expression: (3x^2-7x-6)/(x^2-6x+9)

We start by noticing that both the numerator and denominator are expressions which can be factorised into brackets. Starting with the numerator, we multiply the coefficient of x^2 and the constant term together (3 x -6 = -18). We then look for factors of -18 which add up to -7. We find 2 and -9, so we rewrite the numerator as 3x^2+2x-9x-6. We then look for common factors between the x^2 and x terms. We find 3x from 3x^2 and 9x. We combine and factorise these two terms and then do the same with the remaining terms. This gives us 3x(x-3)+2(x-3). We factorise the (x-3) out and this gives us (3x+2)(x-3). We use the same method to factorise the denominator which leaves us with (3x+2)(x-3)/(x-3)^2. We cancel out (x-3) and obtain the final answer (3x+2)/(x-3).