SOLUTION: Please help me with this problem: Rationalize the denominator. Assume that all expressions under the radical represent positive numbers. 4√7/√5-√3
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Question 383640: Please help me with this problem: Rationalize the denominator. Assume that all expressions under the radical represent positive numbers. 4√7/√5-√3
Answer by jsmallt9(3758) (Show Source): You can put this solution on YOUR website!
Your denominator has two terms. Rationalizing a two term denominator uses the pattern: . The pattern shows us how a binomial, (a+b) or (a-b), can be turned into an expression of perfect squares, !
Your denominator has a minus between the two terms. So it will plat the role of (a-b) with "a" being and "b" being . To rationalize this denominator we will multiply the numerator and denominator by (a+b):
In the numerator we will use the distributive Property to multiply. In the denominator we already know we will get :
which simplifies as follows:
You can already see that the denominator is rational.
We can reduce this fraction by factoring out a 2 in the numerator:
Not only did we rationalize the denominator but we eliminated the fraction entirely!
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