## Ac3 one year ago Simplify the following expression. sqrt((1/(3(1+x)^(1/2))+(1/(3(1-x)^(1/2)))

1. freckles

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

2. Ac3

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

3. Ac3

Forgot to square it

4. Ac3

This is the one.

5. 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

6. Ac3

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

7. Ac3

8. freckles

what did you get?

9. Ac3

$\frac{ 1 }{ 3 }\sqrt{\frac{ 2 }{ 1-x^2 }}$

10. freckles

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

11. 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.

12. freckles

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

13. 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.

14. Ac3

Take this last one for example.

15. Ac3

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

16. Ac3

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

17. freckles

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

18. 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.

19. freckles

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

20. Ac3

oh well, hopefully it's right. Thanks!

21. freckles

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

22. Ac3

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

23. Ac3

Thanks!

24. freckles

np

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