Another AP Calc problem that I’m not getting

I did quotient rule and ended up with 48x^4/(4x^4+2x)^2

The answer is c but I don’t know how it was arrived at.

8_18_2

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7 Responses to Another AP Calc problem that I’m not getting

  1. OSEverything says:

    48x^4/(4x^4+2x)^2 = 4x^2(12x^2)/[2x(2x^3+1)]^2 = 4x^2(12x^2)/[4x^2(2x^3+1)^2] = 12x^2/(2x^3+1)^2

    You had the right answer, but you needed to factor out 4x^2 from the numerator and denominator to simplify.

    • mindweapon says:

      Oh! I see how you did that!

    • Start by dividing the numerator and denominator of the original fraction by 2x.

      • Anon says:

        Factoring immediately makes the problem very simple, not factoring makes it really hard:

        Start:
        4x^4 – 2x
        ————
        4x^4 + 2x

        Step One(factoring):
        2x^3 – 1
        ———-
        2x^3 + 1

        Step Two(Quotient Rule):
        6x^2 * (2x^3 + 1) – (2x^3-1)*6x^2
        —————————————
        (2x^3+1)^2

        Step Three( straight up multiplication ):
        16x^5 + 6x^2 – 16x^5 + 6x^2
        —————————————
        (2x^3+1)^2

        Step Four(Simplying terms):
        12x^2
        ————–
        (2x^3+1)^2

        I still can’t get it without factoring immediately.

      • Anon says:

        Ok, I found the missing part I was breaking when not factoring.

  2. Ryu says:

    Stop trying to take shortcuts! Just break it into simple steps. Don’t try to save paper. If it takes an entire sheet of paper, use it. Paper is cheap.

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