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Divide Equations

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2 Answers

There is more then one way to do this problem.  Since the denominator is a monomial (only one term), I would first separate the problem like this:(-20x^6/-4x^4)+(-24x^4/-4x^4)+(-12x^2/-4x^4)

Next, I would divide within each set of parentheses.

For the first set, -20/-4 = 5, and x^6/x^4 = x^2 (when the same variable is in the numerator and the denominator, you subtract the exponents).  So the first set becomes 5x^2

For the second set, -24/-4 = 6, and x^4/x^4 = 1 (subtracting 4-4 = 0, and x^0 = 1, since anything^0 = 1).  So we get 6 * 1 = 6

For the last set, -12/-4 = 3, and x^2/x^4 =x^-2.  Negative exponents are not permitted in a completely simplified answer, so a term with a negative exponent still needs work.  x^-2 is the same as 1/x^2 (negative exponents get "flipped"- moved from numerator to denominator or denominator to numerator, and then become positive).  So we get  3* 1/x^2 = 3/x^2

Final answer is 5x^2 + 6 + 3/x^2

Comments

I have a question, Amy. Pardon me, if it's a dumb question. Why is that negative exponents are not permitted in a completely simplified answer?? Is there a rule of math I missed that says something about it?

Comment

I can't be sure what form the answer is expected to have.
You could divide the numerator and denominator by -4x2:

-20x6 - 24x4 - 12x2        5x4 + 6x2 + 3
-----------------------  =   ---------------
         -4x4                           x2

Or you could do this:

 -20x6 - 24x4 - 12x2       -20x6      -24x4      -12x2                          3
-----------------------  =  -------  +  ------  +  ------  =  5x2  +  6  +  ---
          -4x4                    -4x4        -4x4       -4x4                           x2