Simplify fully (3x^2 -8x- 3)/(2x^2-6x)

When simplifying algebraic expressions, we should first factorise each term fully to find any common factors. First we should factorise the numerator where 3x²-8x-3 factorises to (3x+1)(x-3). Next, we should factorise the denominator where 2x²-6x factorises to 2x(x-3). Now we see that (x-3) is the highest common factor of both the numerator and denominator, hence we can "cancel" the (x-3) term from both the numerator and denominator. Therefore, the expression simplifies fully to (3x+1)/(2x)