First, factor the numerator, which should be . Now the left side of your equation looks like

Second, cancel the "like" terms - - which leaves us with .

Third, solve for by setting the left-over factor equal to 0, which leaves you with

Separate the four terms into two groups, and then find the GCF of each group.

First group:

Second group:

The GCF of the first group is . Factoring out from the terms in the first group gives us:

The GCF of the second group is . Factoring out from the terms in the second group gives us:

We can rewrite the original expression,

as,

We can factor this as:

Let's split the four terms into two groups, and find the GCF of each group.

First group:

Second group:

The GCF of the first group is . When we divide the first group's terms by , we get: .

The GCF of the second group is . When we divide the second group's terms by , we get: .

We can rewrite the original expression,

as,

The common factor for BOTH of these terms is .

Dividing both sides by gives us:

For each term in this expression, we will notice that each shares a variable of . This can be pulled out as a common factor.

There are no more common factors, and this is the reduced form.

The answer is:

Because the term has a coefficient, you begin by multiplying the and the terms () together: .

Find the factors of that when added together equal the second coefficient (the term) of the polynomial: .

There are four factors of : , and only two of those factors, , can be manipulated to equal when added together and manipulated to equal when multiplied together:

The common factor here is . Pull this out of both terms to simplify:

Here you have an expression with three variables. To factor, you will need to pull out the greatest common factor that each term has in common.

Only the last two terms have so it will not be factored out. Each term has at least and so both of those can be factored out, outside of the parentheses. You'll fill in each term inside the parentheses with what the greatest common factor needs to be multiplied by to get the original term from the original polynomial:

Consider the possible values for (x, y):

(1, 100)

(2, 50)

(4, 25)

(5, 20)

Note that (10, 10) is not possible since the two variables must be distinct. The sums of the above pairs, respectively, are:

1 + 100 = 101

2 + 50 = 52

4 + 25 = 29

5 + 20 = 25, which is the smallest sum and therefore the correct answer.

Because the term doesn’t have a coefficient, you want to begin by looking at the term () of the polynomial: .

Find the factors of that when added together equal the second coefficient (the term) of the polynomial: .

There are seven factors of : , and only two of those factors, , can be manipulated to equal when added together and manipulated to equal when multiplied together:

Multiply both sides by 3:

Distribute:

Subtract from both sides:

Add the terms together, and subtract from both sides:

Divide both sides by :

Simplify: