To add trinomials, identify and group together the like-terms: . Next, factor out what is common between the like-terms:. Finally, add what is left inside the parentheses to obtain the final answer of .

Since there are no like terms in the numerator or in the denominator, you can only combine ther terms on the numerator and denominator so that they are in one quotient. You cannot further combine the variables because each variable is represented by a different letter. You cannot further reduce the integers because they do not have a common factor. 

First, rearrange the order of the problem by grouping like terms together: 

.

Now, combine the like terms: 

To simplify an expression you need to combine like terms.  

So,

and  cannot be combined with anything.

To then rewrite the expression you want to work in alphabetical order, and in decreasing exponential power.

This problem is best simplified by dealing with the fractions separately and then combining. The rules of exponents used are: , , , and .

Remember to distribute the  to each terms and the  to each term then combine the like terms.

Simplify the following expression by combining like terms:

Begin by looking for terms to combine. In this case, we only have 2 terms we can combine. Remember, we can only combine terms that have the same exponent and variable.

In this case, the green colors are the only ones which can be combined:

So our answer is:

To simplify this expression, you must remember to distribute that negative sign to all of the terms of the second parantheses. It should then look like this: . Then, combine like terms. Your answer should be:

Simplify the following expression:

So, we have a big fraction. Don't be intimidated, all we have to do is cancel some parts out and we'll be good.

Begin by looking for pieces that are in common to the top and bottom. I've highlighted them below:

Now, the parts that are in common need to be simplified, but only with eachother. 

Starting with the y's, we simply subtract the bottom exponent from the top exponent.

Do the same with the part in parentheses.

Leave the z's alone because we only have one set of z's and it's on the bottom.

And we get the following:

It is often best to wrok one term at a time before adding. Looking at the first term, notice that we can immediately cancel the  in the numerator by rules of exponents. Also, we can factor out the  in the numerator and cancel it out with the  in the denominator, 

Notice the difference of two squares  in the denominator; It can be factored as follows, 

(It's recommended that you memorize the formula for the difference of two squares, you will see this often).  

Substituting this into the expression, 

Cancel  in the numerator and denominator, 

Now we need to add the two terms. Multiply the second term above and below by  so it has the same denominator as the first term, 

Add the numerators now that they have a common denominator,