How do you rationalize the numerator in this problem?

Question

asked Oct 22, 2019 234k views

1 Answer

Robert Rowntree · Answer 1 · 2019-10-27T10:41:48+0000

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

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

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:

That is our rational expression with a rationalized numerator.

Also, you could just mutiply by:

Either way, our expression is rationalized.