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What is (sqrt(1-x^2)/2) - (x^2-x/sqrt(1-x^2))?    

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xkat123 | Student, Undergraduate | (Level 1) Honors

Posted November 9, 2012 at 1:32 AM via web

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What is (sqrt(1-x^2)/2) - (x^2-x/sqrt(1-x^2))?



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embizze | High School Teacher | (Level 1) Educator Emeritus

Posted November 9, 2012 at 2:33 AM (Answer #1)

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Simplify `sqrt(1-x^2)/2 - (x^2-x)/sqrt(1-x^2)`

Generally you want to write as a single term if possible, with no radicals in the denominator.

One approach is to rationalize the second term and add the fractions:


`=sqrt(1-x^2)/2-((x^2-x)sqrt(1-x^2))/(1-x^2)`  The common denominator is `2(1-x^2)` :




`=((3x+1)sqrt(1-x^2))/(2(1+x))` which does not simplify further.

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