Question

How do you rationalize the numerator in this problem?

Answer 1

To solve this problem, you have to know these two special factorizations:

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Knowing these tells us that if we want to rationalize the numerator. we want to use the top equation to our advantage. Let:

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That tells us that we have:

`(x-y)/(h)`

So, since we have one part of the special factorization, we need to multiply the top and the bottom by the other part, so:

`(x-y)/(h)*(x^2+xy+y^2)/(x^2+xy+y^2)=(x^3-y^3)/(h*(x^2+xy+y^2))`

So, we have:

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That is our rational expression with a rationalized numerator.

Also, you could just mutiply by:

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Either way, our expression is rationalized.