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 .

When dividing polynomials, subtract the exponent of the variable in the numberator by the exponent of the same variable in the denominator.

If the power is negative, move the variable to the denominator instead.

First move the negative power in the numerator to the denominator:

Then subtract the powers of the like variables:

The numerator is equivalent to

The denominator is equivalent to

Dividing the numerator by the denominator, one gets

First let us find a common denominator as follows:

Now we can subtract the numerators which gives us :

So the final answer is

Factor both the numerator and the denominator which gives us the following:

After cancelling we get

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,

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 

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 .

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: