Simplifying radicals containing polynomial fractions

In summary, simplifying radicals containing polynomial fractions involves reducing the radical to its simplest form and simplifying any fractions within the radical. This can be done by factoring the radicand, simplifying fractions, and taking the square root of perfect squares. All radicals containing polynomial fractions can be simplified, but some may require more steps. The purpose of simplifying these radicals is to make expressions easier to solve and identify any further simplifications. There are rules and guidelines to follow when simplifying, such as factoring, simplifying fractions, and checking the answer by squaring it.
  • #1
ddoctor
9
0
no idea how to simplify this one:

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

thanks

dave
 
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  • #2
how about starting with substituting 1 by (x+1)2/(x+1)2
 
  • #3
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.
 

1. What does it mean to simplify radicals containing polynomial fractions?

Simplifying radicals containing polynomial fractions means to simplify the expression by reducing the radical to its simplest form and simplifying any fractions within the radical.

2. How do I simplify radicals containing polynomial fractions?

To simplify radicals containing polynomial fractions, you must first factor the radicand (the number inside the radical) into its prime factors. Then, simplify any fractions within the radical using common factors. Finally, take the square root of any perfect squares within the radical.

3. Can all radicals containing polynomial fractions be simplified?

Yes, all radicals containing polynomial fractions can be simplified. However, some may require more steps and may not simplify to a whole number.

4. What is the purpose of simplifying radicals containing polynomial fractions?

The purpose of simplifying radicals containing polynomial fractions is to make expressions more manageable and easier to solve. It also helps to identify any perfect square factors that can be simplified further.

5. Are there any rules or guidelines for simplifying radicals containing polynomial fractions?

Yes, there are a few rules and guidelines to follow when simplifying radicals containing polynomial fractions. These include factoring the radicand, simplifying any fractions within the radical, and taking the square root of any perfect squares. It is also important to check your answer by squaring it to make sure it simplifies back to the original expression.

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