How do you differentiate #(x^3 - 9x)/(x^2-7x+12)#?

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Answer 1 · 2015-02-17T23:23:20

First, let us simplify the expression

#(x(x^2-9x))/((x-4)(x-3) #

#(x(x+3)(x-3))/((x-4)(x-3) #

#(x(x+3))/(x-4) #

#(x^2+3x)/(x-4) #

Now differentiate using the quotient rule.

#dy/dx=([(x-4)(2x+3)]-[(x^2+3x(1)]))/(x-4)^2 #

#dy/dx=(2x^2-5x-12-x^2-3x)/(x-4)^2 #

#dy/dx=(x^2-8x-12)/(x-4)^2 #