Cancel:

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 :

Use the properties of powers:

We can cancel now:

To easily divide the polynomials, factor the numerator to get 

Then, you can cancel out  since it is present in both the numerator and the denominator, leaving you with just .

First, factor the numerator to get 

Since  is in both the numerator and the denominator, they cancel each other out. This leaves just  as the simplified version of the expression.

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: 

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 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 do this and we leave ,  &  in the denominator and, since there is nothing left in the numerator we put the placeholder, 1, there! 

  so we leave the 1 in the numerator and put the 2 as the coefficient in the denominator. Leaving us with the answer: 

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.

First we will factor the numerator:

Then factor the denominator:

We can re-write the original fraction with these factors and then cancel an (x-5) term from both parts:

First, set up the division as the following:

Look at the leading term  in the divisor and  in the dividend. Divide  by  gives ; therefore, put  on the top:

Then take that  and multiply it by the divisor, , to get .  Place that  under the division sign:

Subtract the dividend by that same  and place the result at the bottom. The new result is , which is the new dividend.

Now,  is the new leading term of the dividend.  Dividing  by  gives 5.  Therefore, put 5 on top:

Multiply that 5 by the divisor and place the result, , at the bottom:

Perform the usual subtraction:

Therefore the answer is  with a remainder of , or .