SOLUTION: I have to divide and check. Could someone please help me? Divide and check showing work. (4x^4-4x^2-3)/(2x^2-3)

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Question 402777: I have to divide and check. Could someone please help me?
Divide and check showing work.
(4x^4-4x^2-3)/(2x^2-3)
Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!

%284x%5E4-4x%5E2-3%29%2F%282x%5E2-3%29

first factor %284x%5E4-4x%5E2-3%29:
replace -4x%5E2 with 2x%5E2-6x%5E2

4x%5E4+%2B+2x%5E2+-+6x%5E2+-3
Group the first two terms together and the last two terms together like this:
%284x%5E4+%2B+2x%5E2%29+%2B+%28-6x%5E2-3%29
Factor a 2x%5E2 out of the first group and factor a -3 out of the second group.
2x%5E2%282x%5E2+%2B+1%29+%2B+%28-3%29%282x%5E2+%2B+1%29
Now since we have a common term %282x%5E2+%2B+1%29 we can combine the two terms.
%282x%5E2+-3%29%282x%5E2+%2B+1%29

so, now your expression will look like this:

%282x%5E2+-3%29%282x%5E2+%2B+1%29%2F%282x%5E2-3%29

now, reduce

cross%28%282x%5E2+-3%29%29%282x%5E2+%2B+1%29%2Fcross%28%282x%5E2-3%29%29

%282x%5E2+%2B+1%29