Often the algebra associated with the quotient rule in calculus is more difficult than the act of applying the quotient rule. Recall that the quotient rule gives you a way of finding the derivative for fractional functions or quotients of functions, but frequently after you apply the quotient rule you are left with an algebraic mess that needs to be further simplified or factored.

What follows is the step by step algebraic simplification that is required after applying the quotient rule to a particular rational function which also happens to be a complex fraction. The key step was to find the common denominator inside the parentheses and use laws of exponents to further simplify the expression.

Thanks for showing each of the algebra steps. Teachers are sometimes really bad about not showing you every step. Could you show us the steps that were involved in using the quotient rule? Thanks for your step-by-step way of doing things.

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