# simple rearrangement which i cant do!

• Dec 2nd 2010, 11:04 AM
situation
simple rearrangement which i cant do!
how is this: (4+x^2)/sqrt(4+x^2)
the same as sqrt(4+x^2)
?? could someone explain step by step? thanks :)
• Dec 2nd 2010, 11:13 AM
tonio
Quote:

Originally Posted by situation
how is this: (4+x^2)/sqrt(4+x^2)
the same as 4+x^2
?? could someone explain step by step? thanks :)

Hint: for positive $\displaystyle a\in\mathbb{R}\,,\,\,\frac{a}{\sqrt{a}}=\sqrt{a}$ . Prove it!

Tonio

Ps. By the way, your quiestion is incorrect, of course.
• Dec 2nd 2010, 11:14 AM
e^(i*pi)
If you let $\displaystyle u = \sqrt{4+x^2}$ then you get $\displaystyle \dfrac{u^2}{u}$ which is u.

Alternatively, recall that $\displaystyle a = \sqrt{|a|}\sqrt{|a|}$
• Dec 2nd 2010, 11:15 AM
harish21
Quote:

Originally Posted by situation
how is this: (4+x^2)/sqrt(4+x^2)
the same as 4+x^2
?? could someone explain step by step? thanks :)

do you mean $\displaystyle \dfrac{4+x^2}{\sqrt{4+x^2}}=4+x^2$??

That is not true...

Actually $\displaystyle \dfrac{4+x^2}{\sqrt{4+x^2}}=\sqrt{4+x^2}$
• Dec 2nd 2010, 11:16 AM
situation
Quote:

Originally Posted by e^(i*pi)
If you let $\displaystyle u = \sqrt{4+x^2}$ then you get $\displaystyle \dfrac{u^2}{u}$ which is u.

Alternatively, recall that $\displaystyle a = \sqrt{|a|}\sqrt{|a|}$

god i feel stupid now! thank you :)
• Dec 2nd 2010, 11:17 AM
situation
Quote:

Originally Posted by harish21
do you mean $\displaystyle \dfrac{4+x^2}{\sqrt{4+x^2}}=4+x^2$??

That is not true...

Actually $\displaystyle \dfrac{4+x^2}{\sqrt{4+x^2}}=\sqrt{4+x^2}$

that is what i meant sorry just couldnt see it!