Simplifying This Expression

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August 14th 2011, 03:24 PM
YoungMarbleGiant

Simplifying This Expression

I have the following:

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

How do you go about simplifying this? DO you simplify each part individually by the 1/2 exponent? Thank you for any tips.
August 14th 2011, 03:36 PM
anonimnystefy

Re: Simplifying This Expression

you can't do it individually because it is the same as:
$\sqrt{4-\frac{1}{(x+1)^2}}$
$\sqrt{a-b}\neq\sqrt{a}-\sqrt{b}$
to do this you have to subtract $4-\frac{1}{(x-1)^2}$ .can you do that?
August 14th 2011, 03:52 PM
YoungMarbleGiant

Re: Simplifying This Expression

Quote:

Originally Posted by anonimnystefy

you can't do it individually because it is the same as:
$\sqrt{4-\frac{1}{(x+1)^2}}$
$\sqrt{a-b}\neq\sqrt{a}-\sqrt{b}$
to do this you have to subtract $4-\frac{1}{(x-1)^2}$ .can you do that?

To get $\frac{4(x-1)^{2} - 1}{(x-1)^{2}}$ ... ?

If that's correct, am I then able to take each term to the 1/2 exponent because it's all expressed with the same denominator?
August 14th 2011, 05:12 PM
Prove It

Re: Simplifying This Expression

Quote:

Originally Posted by YoungMarbleGiant

To get $\frac{4(x-1)^{2} - 1}{(x-1)^{2}}$ ... ?

If that's correct, am I then able to take each term to the 1/2 exponent because it's all expressed with the same denominator?

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.
August 14th 2011, 05:42 PM
YoungMarbleGiant

Re: Simplifying This Expression

Quote:

Originally Posted by Prove It

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.

So it simplifies to the square root of the whole numerator, over (x-1)... is that correct? Sorry if I've not followed you here.
August 14th 2011, 06:50 PM
Prove It

Re: Simplifying This Expression

Quote:

Originally Posted by YoungMarbleGiant

So it simplifies to the square root of the whole numerator, over (x-1)... is that correct? Sorry if I've not followed you here.

The denominator should be |x - 1|, otherwise you're correct.