2x + 3/x - 2?

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Answer 1 · 2017-06-15T17:15:46

I assume you mean to evaluate...

#(2x + 3)/(x - 2)#

whatever "evaluate" means here.

#= (2x - 4 + 7)/(x-2)#

#= (2(x-2))/(x-2) + 7/(x-2)#

#= 2 + 7/(x-2)#

In general its derivative would follow the power rule:

#d/(dx)[x^n] = nx^(n-1)#.

This can be rewritten as #2 + 7(x-2)^(-1)#. Thus...

But of course, actual order of operations would indicate at face value...

#2x + 3/x - 2 = 2x + 3x^(-1) - 2#

whose derivative is #2 - 3/x^2# and indefinite integral is #x^2 + 3ln|x| - 2x + C#.