Solve (x^2 - 4)/(2x+4)

The common mistake the students make is to simplify the fraction before factorising numerator and denominator. Here, we need to see that the numerator: x^2 - 4 is a difference between squares, i.e. A^2 - B^2 = (A+B)(A-B). Having recognised that, x^2-4 = (x+2)(x-2) and this can be proved by doing the inverse multiplication back to the original question. Similarly (but easier), the denominator: 2x+4 -> the two terms have a 2 in common, so it can be rewritten: 2(x+2)At this point, and ONLY at this point, this can be simplified by recognising that the factor x+2 is present both at numerator and at denominator.So the final result is: (x-2)/2Many students attempt to cancel out terms before factorising, so it is important to show that this is not the right procedure.