Hi Bailey,

Use the distributive property in reverse here.

Factor out the 3 in both terms of the numerator.

3 ÷ 3 = 1. Any number divided by itself equals 1.

The simplified result is just all that's left over

once the 3s are canceled out.

3 ± 3√17    3(1 ± √17)      3    1 ± √17   1 ± √17    -1 ± √17

_______  = __________ = ___ ∙ ______ = ______ = ________

    -12              3(-4)           3        -4            -4              4

However, it would be unusual for the denominator to be left negative. That negative sign would most likely be absorbed into the numerator, as a matter of convention.

Wow.  I am still very confused.  Why would you divide?  This has been the hardest thing in math I have done.  Thanks for answering, though!

What you have to do is take the question into the factors of each of the numbers. Pei-Hsin Lin described it well, and I will do it differently, but based off of hers.

3±3√17

 ______

    -12

Look at the factors, the low numbers that make up each number. The top ones are the lowest they can go, (17*1, 3*1, they are their factors) but 12 you can take down. It can be divided by 2, 12/2=6

So 6*2 is a factor. But can you go lower? divide 6/2, and it equals 3

So 3*2, and then add on the two from the first quotient. 3*2*2

All of these factors are still equal to 12, the original problem.

Now, put the factors into the problem, like so.

3±3√17

 ______

    -3*2*2

You can cancel out the threes from the top part of the equation now, since there is a three on the top and bottom! Hope this helps! (And that it was not incorrect!)

Yours, Panzerkampfwagen

Ok.  I have studied this so much, but I still cannot understand this last part.  Thank you SO much for taking the time to answer (I mean this sincerely).