- #1
Econguy
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I am taking an online Introductory Calculus course. I have a decent understanding thus far, however, the problem I'm working on gets somewhat messy and I am having a difficult time simplyifing the answer.
f"(x) = (x^2 + 9)^2 (-2x) - [(9 - x^2)(2)(x^2 + 9)(2x)]/(x^2 + 9)^4
the solutions manual I have been given gives the following simplified answer:
= (2x)(x^2 + 9) [-(x^2 + 9) -2(9 - x^2)]/(x^2 +9)^4
= 2x(x^2 - 27)/(x^2 + 9)^3
I am having a difficult time understanding the factoring involved in the algebraic simplification. I understand how to factor by grouping, trinomials etc. but I just can't seem to understand this. If someone could help fill in the missing steps that my solutions manual doesn't include it would be a great help. Even providing an explanation on the steps involved would help me understand the process much better.
Thanks
f"(x) = (x^2 + 9)^2 (-2x) - [(9 - x^2)(2)(x^2 + 9)(2x)]/(x^2 + 9)^4
the solutions manual I have been given gives the following simplified answer:
= (2x)(x^2 + 9) [-(x^2 + 9) -2(9 - x^2)]/(x^2 +9)^4
= 2x(x^2 - 27)/(x^2 + 9)^3
I am having a difficult time understanding the factoring involved in the algebraic simplification. I understand how to factor by grouping, trinomials etc. but I just can't seem to understand this. If someone could help fill in the missing steps that my solutions manual doesn't include it would be a great help. Even providing an explanation on the steps involved would help me understand the process much better.
Thanks
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