How do I manipulate a formula to get 1/√(w²+4)?

[greg997]

Can someone show me in steps how to manipulate this formula in attachement to obtain 1/(sqr(w^2+4)? Thanks

 

[jack action]

The two equations are not equal. Just replace w by any value and you'll see that both equations give different answers.

 

[Mentallic]

The best you can really get is:

$$\frac{\sqrt{4-w^2}}{w^2+4}$$

 

[Mentallic]

You must have made a typo. The expression should be,

$$\sqrt{\left(\frac{2}{w^2+4}\right)^2+\left(\frac{w}{w^2+4}\right)^2}$$

 

[greg997]

You must have made a typo. The expression should be,

$$\sqrt{\left(\frac{2}{w^2+4}\right)^2+\left(\frac{w}{w^2+4}\right)^2}$$

Hmm, that's quite possible. Then how to get that solution?

 

[Mentallic]

Well I can't just give you the answer, you need to show an attempt at solving the problem first.

But I can give you some hints, you can most certainly find the answer by using a combination of these rules:

$$\sqrt{\frac{a}{b}}=\frac{\sqrt{a}}{\sqrt{b}}$$

$$\sqrt{a^2b}=|a|\sqrt{b}$$ (the |a| means the positive of a, but remember that for any real number n, n² is always positive).

$$\frac{a}{c}+\frac{b}{c}=\frac{a+b}{c}$$

$$\frac{\sqrt{a}}{a}=\frac{1}{\sqrt{a}}$$


Good luck!

 

[greg997]

Hello, I am sorry but it just does not work. What am I doing work? Thanks

 

[Cyosis]

You're adding fractions, but you're multiplying numerators.

 

[greg997]

AAA, stupid me:) Thanks