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.
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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.
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.
Oh! I see how you did that!
Start by dividing the numerator and denominator of the original fraction by 2x.
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.
Thanks Anon!
Ok, I found the missing part I was breaking when not factoring.
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.