Can you show this? (sqrt(2x^2+1))/(x)=sqrt(2+1/x^2).This seems like basic algebra, but I can't really manage to deal with the sqrt sign and prove this.

katdoringlo 2022-09-12 Answered
Can you show this?
Show that
2 x 2 + 1 x = 2 + 1 / x 2 .
This seems like basic algebra, but I can't really manage to deal with the sqrt sign and prove this.
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Answers (2)

Andrejkoxg
Answered 2022-09-13 Author has 20 answers
I think it's wrong.
Try x = 1.
By the way,
2 x 2 + 1 x = 2 + 1 x 2
for x>0 and
2 x 2 + 1 x = 2 + 1 x 2
for x<0.
The both equalities we can write so:
2 + 1 x 2 = 2 x 2 + 1 x 2 = 2 x 2 + 1 | x |

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Frida Faulkner
Answered 2022-09-14 Author has 2 answers
1) x > 0 , the equality is OK.
2) x < 0, LHS is negative, RHS positive.
LHS: 2 x 2 + 1 x =
x 2 ( 2 + 1 x 2 ) x =
| x | 2 + 1 x 2 x =
| x | x 2 + 1 x 2 .
Note:
| x | x = 1 for x > 0 ;
| x | x = 1 for x < 0.

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