# simple rearrangement which i cant do!

Printable View

• December 2nd 2010, 12:04 PM
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 :)
• December 2nd 2010, 12:13 PM
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 $a\in\mathbb{R}\,,\,\,\frac{a}{\sqrt{a}}=\sqrt{a}$ . Prove it!

Tonio

Ps. By the way, your quiestion is incorrect, of course.
• December 2nd 2010, 12:14 PM
e^(i*pi)
If you let $u = \sqrt{4+x^2}$ then you get $\dfrac{u^2}{u}$ which is u.

Alternatively, recall that $a = \sqrt{|a|}\sqrt{|a|}$
• December 2nd 2010, 12:15 PM
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 $\dfrac{4+x^2}{\sqrt{4+x^2}}=4+x^2$??

That is not true...

Actually $\dfrac{4+x^2}{\sqrt{4+x^2}}=\sqrt{4+x^2}$
• December 2nd 2010, 12:16 PM
situation
Quote:

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

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

god i feel stupid now! thank you :)
• December 2nd 2010, 12:17 PM
situation
Quote:

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

That is not true...

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

that is what i meant sorry just couldnt see it!