SOLUTION: Simplify by rationalizing the denominator. y over sqrt 7 plus sqrt 3

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Question 595614: Simplify by rationalizing the denominator.
y over sqrt 7 plus sqrt 3

Answer by jsmallt9(3758) About Me  (Show Source):
You can put this solution on YOUR website!
y%2F%28sqrt%287%29%2Bsqrt%283%29%29
Rationalizing two-term denominators makes use of the following pattern:
%28a%2Bb%29%28a-b%29+=+a%5E2+-+b%5E2
This pattern shows us how to take a two-term expression, an a+b or a-b, multiply it by something and get an expression made up of all perfect squares, a%5E2-b%5E2. Since your two-term denominator has a "+" between the terms it will play the role of a+b. So we need to multiply it (and the numerator) by a-b:


We already know that the denominator will be a%5E2-b%5E2. On top we just distribute the y:
%28y%2Asqrt%287%29-y%2Asqrt%283%29%29%2F%28%28sqrt%287%29%29%5E2-%28sqrt%283%29%29%5E2%29
which simplifies as follows:
%28y%2Asqrt%287%29-y%2Asqrt%283%29%29%2F%287-3%29
%28y%2Asqrt%287%29-y%2Asqrt%283%29%29%2F4