`f(x) = (x^2 + 5x + 6)/(x^2 - 4)` Find the derivative of the algebraic function.

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Chapter 2, 2.3 - Problem 26 - Calculus of a Single Variable (10th Edition, Ron Larson).
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mathace | (Level 3) Assistant Educator

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Given `f(x)=(x^2+5x+6)/(x^2-4)`

Simplify the function to `f(x)=((x+2)(x+3))/((x-2)(x+2))=(x+3)/(x-2)`

Find the derivative using the Quotient Rule.

`f'(x)=((x-2)(1)-(x+3)(1))/(x-2)^2`

`f'(x)=(x-2-x-3)/(x-2)^2` 

`f'(x)=-5/(x-2)^2` 

The derivative will exist for all real numbers except at x=2.

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