First let us find a common denominator as follows:

Now we can subtract the numerators which gives us :

So the final answer is

We can accomplish this division by re-writing the problem as a fraction.

The denominator will distribute, allowing us to address each element separately.

Now we can cancel common factors to find our answer.

Divide the leading coefficients to get the first term of the quotient:

, the first term of the quotient

Multiply this term by the divisor, and subtract the product from the dividend:

Repeat these steps with the differences until the difference is an integer. As it turns out, we need to repeat only once:

, the second term of the quotient

, the remainder

Putting it all together, the quotient can be written as .

First, rewrite this problem so that the missing term is replaced by

Divide the leading coefficients:

, the first term of the quotient

Multiply this term by the divisor, and subtract the product from the dividend:

Repeat this process with each difference:

, the second term of the quotient

One more time:

, the third term of the quotient

, the remainder

The quotient is and the remainder is ; this can be rewritten as a quotient of

The numerator can be factored into

,

which when divided by ,

gives us .

Alternate method: Long division of the numerator by the denominator gives the same answer.

7 in the denominator is a common factor of the three coefficients in the numerator, which allows you to divide out the 7 from the denominator:

Then divide by :

When we divide a complex set of variables which are all being multiplied by another similar set of variables which are being multiplied (as in our problem!) we are able to handle each separate variable as it's own division problem. So, that the complex fraction

is really 4 separate fractions:

And, when we divide like terms with exponents, we subtract the powers! So, we are able to eliminate the , we leave one in the denominator and one in the numerator! is 5, so we leave the 5 in the numerator as well. This leaves us with the answer:

We are dividing the polynomial by a monomial. In essence, we are dividing each term of the polynomial by the monomial. First I like to re-write this expression as a fraction. So,

So now we see the three terms to be divided on top. We will divide each term by the monomial on the bottom. To show this better, we can rewrite the equation.

Now we must remember the rule for dividing variable exponents. The rule is So, we can use this rule and apply it to our expression above. Then,

In order to divide these polynomials, we will need to factorize both the top and the bottom expressions.

Cancel out the common terms in the numerator and denominator.

The answer is:

4 goes into 24, 12, 8, and 4.

Similarly, the smallest exponent of x in the four terms is 2, and the smallest exponent of y in the four terms is 1.

Hence the GCF must be .