Factorise and simplify (6x-42)/((x^2)-49)

When we factorise, we are trying to put a long expression into a couple of brackets to make it neater and easier to work with. It is the opposite to multiplying out brackets. To start off with, we will factorise both the top and the bottom expressions. This will leave us with 6(x-7) on the top as 6 is the common factor in both terms and when multiplied by (x-7) it gives us our original expression back. And for the bottom we get (x-7)(x+7) as it is the difference of two squares, and we can also see that if we were to expand these brackets following the F.O.I.L method, we would return to our original expression. So now we have factorised both expressions we want to leave in its simplest form which often involves cancelling when working with fractions. Therefore we can cancel the (x-7) which appears on the top and the bottom. This will leave us with our final answer which is 6/(x+7).