A druggist needs 25 liters of a solution that is 16% iodine. She has one solution that is 12 % iodine and another that is 37 %.
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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:
So, since we have one part of the special factorization, we need to multiply the top and the bottom by the other part, so:
So, we have:
That is our rational expression with a rationalized numerator.
Also, you could just mutiply by:
Either way, our expression is rationalized.