# derivative using quotient rule

• February 16th 2010, 06:47 PM
maybnxtseasn
derivative using quotient rule
how do i know if a derivative when solved using the quotient rule will need to be simplified or not by factoring out a variable (i probably worded this wrong)
example
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f'(x) = (x^3+5x+3)/(x²-1)

how do i know if while im solving this if i will need to factor something out?
• February 16th 2010, 06:50 PM
pickslides
Your function here cannot evenly factor.

$\frac{x^3+5x+3}{x^2-1} = \frac{x^3+5x+3}{(x-1)(x+1)}$

The numerator does not have any similar factors to the denominator.