Ok, Let S See If This Helps I Ll Try to Talk You Through It

Ok, let’s see if this helps…I’ll try to talk you through it

Given the example:

(notice the denominators are different, so we cannot just add the numerators)

The first thing you do is factor the denominators and rewrite

Now that the denominators are factored you want to see what factors are “like”, meaning which factors are in both denominators. Remember this means that they are exactly the same when in the parenthesis, the signs and the numbers. In this example (x + 1) is the same because it is in the left expression as well as the right expression. So we do not have to worry about that. However the expression on the left needs to be multiplied by

(x – 4). We are going to multiply both numerator and denominator by (x – 4).

We also need to multiply the expression on the right by (x – 1).

(this multiplication of the expressions can be done in one step)

Ok, so now what we are going to do is actually multiply out the numerators using either distribution (best property =] ) or FOIL (this depends on the situation). In this case we will distribute the 2x to the (x - 4) and we will distribute the 6 to the (x – 1). Do not multiply out the denominators, leave them in factored form.

At this point our denominators are the same, so we are able to add or subtract the numerators. The denominator will remain (x – 4)(x -1)(x + 1). (order doesn’t matter based on the commutative property of multiplication =] )

I combined the expressions into one expression, but I have not simplified the numerators. Be careful because we are subtracting you need to remember to KCO. I will do that now.

At this point you are going to add (or combine) the like terms in the numerator

Since there is an obvious GCF, I’m going to see if the numerator can be factored.

I see that it cannot be factored any further so I can leave this as my answer or I can leave the non-factored version as my answer. Either is sufficient. 99% of the time you will not be able to cancel out at the end of the problem. The important thing is that YOU DO NOT ATTEMPT TO CANCEL OUT UNTIL THE VERY, VERY, VERY LAST STEP!!! You only do the cancelling out with multiplication and division. This is extremely important.