I have the following:

$\displaystyle {(4 - \frac{1}{(x+1)^{2}})^{1/2}}$

How do you go about simplifying this? DO you simplify each part individually by the 1/2 exponent? Thank you for any tips.

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- Aug 14th 2011, 03:24 PMYoungMarbleGiantSimplifying This Expression
I have the following:

$\displaystyle {(4 - \frac{1}{(x+1)^{2}})^{1/2}}$

How do you go about simplifying this? DO you simplify each part individually by the 1/2 exponent? Thank you for any tips. - Aug 14th 2011, 03:36 PManonimnystefyRe: Simplifying This Expression
you can't do it individually because it is the same as:

$\displaystyle \sqrt{4-\frac{1}{(x+1)^2}}$

$\displaystyle \sqrt{a-b}\neq\sqrt{a}-\sqrt{b}$

to do this you have to subtract $\displaystyle 4-\frac{1}{(x-1)^2}$.can you do that? - Aug 14th 2011, 03:52 PMYoungMarbleGiantRe: Simplifying This Expression
- Aug 14th 2011, 05:12 PMProve ItRe: Simplifying This Expression
As you were told above, the square root of a sum/difference is NOT equal to the sum/difference of the square roots. So you can't take each term in the numerator to the 1/2 power.

However, the square root of a product/quotient DOES equal the product/quotient of the square roots. So you CAN take the square root of the numerator and the square root of the denominator. - Aug 14th 2011, 05:42 PMYoungMarbleGiantRe: Simplifying This Expression
- Aug 14th 2011, 06:50 PMProve ItRe: Simplifying This Expression