The first thing to check for is if there are any common factors on the top and bottom. You do this by factorising the top and bottom parts of the fraction.
If there are take them out and cancel them. For example - our fraction has an \(x\) in the and an \(x\) at the bottom so we can cancel both \(x\) 's.
The second step is to see if you can factorise both the top and bottom parts of your fraction.
If there are any factors that are the same in both the top and the bottom of the fraction then you can cancel these as well.In our example you can see that \((x-2)\) is in both the numerator and the denominator. So we can cancel this bracket out as well.
Now there is nothing more that you can cancel in the fraction - so it has been simplified.
Remember you cannot cancel over a plus or minus sign. Also check out the grade 10 chapter on algebra for help with algebraic fractions.