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

First I would look for common factors in either the numerator or the denominator. The denominator has the common factor of (2x) so i would factorise it by 2x in order to give (3x²-8x-3)/(2x)(x-3)Then I would look for a quadratic to factorise the numerator. As the first term is 3x² I know the two 'x' terms must be 3x and x. Furthermore, the final term is -3 which means that the second terms of the quadric must be plus or minus 3 and plus or minus 1. As the final term is a negative that also means that the symbols must be different. With this information, I know that it needs to be factorised into (3x+1)(x-3). This will leave -8x when multiplied out as 3x*-3=-9x and x*1=x. x-9x=-8xThis leaves us with the equation (3x+1)(x-3)/(2x)(x-3). As both the numerator and denominator have the term (x-3) they can cancell out to leave the final answer as 3x+1/2x