Simplifying radicals containing polynomial fractions

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SUMMARY

The discussion focuses on simplifying the radical expression sqrt[1 - ((x-1)²/(x+1)²)]. The solution involves substituting 1 with (x+1)²/(x+1)², leading to the expression [(x+1)² - (x-1)²]/(x+1)². After expanding and combining the polynomial expressions in the numerator, the final simplified form is 2 * sqrt(x)/(x+1). This method demonstrates a clear approach to handling polynomial fractions within radicals.

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Students and educators in algebra, mathematicians focusing on polynomial functions, and anyone looking to enhance their skills in simplifying complex expressions involving radicals and fractions.

ddoctor
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no idea how to simplify this one:

sqrt [1- [(x-1)^2/(x+1)^2]]

thanks

dave
 
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how about starting with substituting 1 by (x+1)2/(x+1)2
 
ok. thanks! so then i get [(x+1)^2 - (x-1)^2/ (x+1)^2] . after that i expanded the polynomial expressions in the numerator and combined them. that simplifies to sqrt [(4x)/ (x+1)^2] or 2 * sqrt (x)/ (x+1). easy enough.
 

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