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How do you rationalize the numerator in this problem?

How do you rationalize the numerator in this problem?-example-1
User Mcont
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1 Answer

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


image

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


image

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:


image

That is our rational expression with a rationalized numerator.

Also, you could just mutiply by:


image

Either way, our expression is rationalized.

User Robert Rowntree
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6.5k points