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- Ac3

Simplify the following expression.
sqrt((1/(3(1+x)^(1/2))+(1/(3(1-x)^(1/2)))

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- Ac3

Simplify the following expression.
sqrt((1/(3(1+x)^(1/2))+(1/(3(1-x)^(1/2)))

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- freckles

\[\sqrt{\frac{1}{3(1+x)^\frac{1}{2}}+\frac{1}{3(1-x)^\frac{1}{2}}}\]
is this right?

- Ac3

\[\sqrt{(\frac{ 1 }{ 3(1+x)^{1/2}})^{2}+(\frac{ 1 }{ 3(1-x)^{1/2} })^{2}}\]

- Ac3

Forgot to square it

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- Ac3

This is the one.

- freckles

\[\text{ by law of exponents you can write } (\frac{1}{3(1+x)^\frac{1}{2}})^2=\frac{1^2}{3^2(1+x)^\frac{2}{2}}...\]
you can do the same with the other term inside that big square root thingy

- Ac3

I know how to do it. I just want to see what someone else gets.

- Ac3

I don't like my answer.

- freckles

what did you get?

- Ac3

\[\frac{ 1 }{ 3 }\sqrt{\frac{ 2 }{ 1-x^2 }}\]

- freckles

that is what I have too..
\[\sqrt{\frac{1}{9(1+x)}+\frac{1}{9(1-x)}} \\ \sqrt{\frac{1}{9}} \sqrt{\frac{1}{1+x}+\frac{1}{1-x}} \\ \frac{1}{3} \sqrt{\frac{2}{1-x^2}} \]

- Ac3

The reason I don't like it. Is because in these problems that I've been doing we tend to get rid of x in the expression through simplifying.

- freckles

you can't get rid of x here though ...

- Ac3

Since it's not disappearing makes me wonder that I did something wrong. However no matter how many times I go back I can't find anything wrong with my math.

- Ac3

Take this last one for example.

- Ac3

\[\sqrt{\frac{ (sinx)^2 }{ 2 }+(cosx)^2+\frac{ (sinx)^2 }{ 2 }}\]

- Ac3

in that one we get rid of x. It all simplifies down to 1.

- freckles

right because sin^2(x)+cos^2(x)=1
and the sqrt(1)=1

- Ac3

exactly so that's why I'm a bit worried that we may be wrong. We usually tend to get rid of the x from inside of the radical at least.

- freckles

if you want to rationalize the denominator you can but that would still leave x inside the radical in the numerator

- Ac3

oh well, hopefully it's right. Thanks!

- freckles

but the simplification you have is so far right
if the problem really is:
\[\sqrt{(\frac{1}{3(1+x)^\frac{1}{2}})^2+(\frac{1}{3(1-x)^\frac{1}{2}})^2}\]

- Ac3

yes it is. It is right. On the next part of the problem it makes sense.

- Ac3

Thanks!

- freckles

np

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