Question

I'm stuck right here:
(x^2-(sqrt(x^2+4))(2+sqrt(x^2+4)))/(4x(sqrt(x^2+4))(2+sqrt(x^2+4)))

Answer 1

\(\Large \dfrac{(x^2-(\sqrt{(x^2+4)})(2+\sqrt{(x^2+4)}))}{(4x(\sqrt{(x^2+4)})(2+\sqrt{(x^2+4)}))}\)

i can see \((2+\sqrt{(x^2+4)})\)
getting cancelled...

Answer 2

or did you purposely multiplied numerator and denominator by
\(2+\sqrt{x^2+4}\)
?

Answer 3

The one that should be multiplied in the numerator is (sqrt(x^2+4) and (2+sqrt(x^2+4))

Answer 4

may i know the original question ? :)

Answer 5

Here:

Answer 6

so it'll be
\(\Large \dfrac{x^2-(\sqrt{(x^2+4)})(2+\sqrt{(x^2+4)})}{(4x(\sqrt{(x^2+4)})(2+\sqrt{(x^2+4)}))}\)

lets try to simplify the numerator

\(x^2-(\sqrt{(x^2+4)})(2+\sqrt{(x^2+4)}) = x^2 - 2\sqrt{(x^2+4)} -\sqrt{(x^2+4)}\sqrt{(x^2+4)} \)

Answer 7

= \(x^2 -2\sqrt{(x^2+4)} - (x^2 +4)\)

notice the x^2 term gets cancelled....
makes sense till now?

Answer 8

Yes

Answer 9

so what does numerator simplify to ?

Answer 10

it will become -2(sqrt(x^2+4)) -4

Answer 11

correct and what if you factor out -2 from that ?

Answer 12

-2(sqrt(x^2+4) +2)

Answer 13

so we now have
\(\large \dfrac{-2((2+\sqrt{(x^2+4)})}{(4x(\sqrt{(x^2+4)})(2+\sqrt{(x^2+4)}}\)

and now
\((2+\sqrt{(x^2+4)}\)
gets cancelled! :)

Answer 14

Thanks you!!!! :D

Answer 15

welcome ^_^