Asked by Anonymous
How do I rationalize the dinominator on this (x^2 +y^2)/(√(x^2 +y^2 +1)-1)
Answers
Answered by
oobleck
multiply top and bottom by the conjugate:
(x^2 +y^2)/(√(x^2 +y^2 +1)-1) * (√(x^2 +y^2 +1)+1)/(√(x^2 +y^2 +1)+1)
=(x^2+y^2)(√(x^2 +y^2 +1)+1)/((x^2+y^2+1)-1)
= (x^2+y^2)(√(x^2 +y^2 +1)+1)/(x^2+y^2)
= √(x^2 +y^2 +1)+1
(x^2 +y^2)/(√(x^2 +y^2 +1)-1) * (√(x^2 +y^2 +1)+1)/(√(x^2 +y^2 +1)+1)
=(x^2+y^2)(√(x^2 +y^2 +1)+1)/((x^2+y^2+1)-1)
= (x^2+y^2)(√(x^2 +y^2 +1)+1)/(x^2+y^2)
= √(x^2 +y^2 +1)+1
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