Question

(x/sqrt(x^2+1)+1)/(x+sqrt(x^2+1)) simplify (x/sqrt(x^2+1)+1)/(x+sqrt(x^2+1)) simplify @Mathematics

Answer 1

plz show steps

Answer 2

type using equation tool

Answer 3

\[\frac{\frac{x}{\sqrt{x^2+1}+1}}{x+\sqrt{x^2+1}}\]?

Answer 4

yeah it looks like that

Answer 5

except the 1 is outside the squareroot

Answer 6

numerator

Answer 7

so both ones?

Answer 8

Is it sqrt for both the ones?

Answer 9

here you type go to equation button below
and for fraction do frac{something}{stuff}
and if you want square root of something do sqrt{something}

Answer 10

\[\frac{\frac{x}{\sqrt{x^2+1}}+1}{x+\sqrt{x^2+1}}\]

Answer 11

multiply top and bottom by sqrt(x^2+1)

Answer 12

\[(x+1)^{-1}\]

Answer 13

\[\frac{\frac{x}{\sqrt{x^2+1}}+1}{x+\sqrt{x^2+1}} \cdot \frac{\sqrt{x^2+1}}{\sqrt{x^2+1}}\]

Answer 14

ok

Answer 15

\[\frac{x+\sqrt{x^2+1}}{x \sqrt{x^2+1}+(x^2+1)}\]

Answer 16

im following

Answer 17

\[\frac{x+\sqrt{x^2+1}}{x \sqrt{x^2+1}+(x^2+1)} \cdot \frac{x \sqrt{x^2+1}-(x^2+1)}{x \sqrt{x^2+1}-(x^2+1)}\]
\[\frac{(x+\sqrt{x^2+1})(x \sqrt{x^2+1}-(x^2+1))}{x^2 (x^2+1)-(x^2+1)^2}\]
\[=\frac{(x+\sqrt{x^2+1})(x \sqrt{x^2+1}-(x^2+1))}{x^4+x^2-(x^4+2x^2+1)}\]
\[=\frac{(x+\sqrt{x^2+1})(x \sqrt{x^2+1}-(x^2+1))}{-x^2-1}\]
\[=\frac{(x+\sqrt{x^2+1})(x \sqrt{x^2+1}-(x^2+1))}{-(x^2+1)}\]

Answer 18

\[=\frac{x^2 \sqrt{x^2+1}-x(x^2+1)+x(x^2+1)-(x^2+1)^{\frac{1}{2}+1}}{-(x^2+1)}\]
\[=\frac{x^2 \sqrt{x^2+1}-(x^2+1)^\frac{3}{2}}{-(x^2+1)}\]

Answer 19

\[=\frac{\sqrt{x^2+1}(x^2-(x^2+1))}{-(x^2+1)}=\frac{\sqrt{x^2+1}(-1)}{-(x^2+1)}\]

Answer 20

ok it makes sense

Answer 21

\[=\frac{\sqrt{x^2+1}}{x^2+1}\]

Answer 22

does it really
i did a lot of stuff
you followed that?
if so thats real good

Answer 23

im double checking

Answer 24

ok i did multiply top and bottom by the conjugate of the bottom to rationalize the bottom did you notice that?

Answer 25

you know after i got rid of the compound fraction action

Answer 26

yeah i got those parts

Answer 27

i just wanted to compare with my answer

Answer 28

ok

Answer 29

i actually had to think on can i simplify this more after i got to a certain point
i like paused for 5 seconds lol

Answer 30

i know what you mean

Answer 31

my paper right now is filled with a bunch of unnecesary moves

Answer 32

i made it worse than the original statement

Answer 33

sometimes it takes unnecessary steps to see you are going to a deadend

Answer 34

yeah i know what you mean, but i really messed up this problem but i got a different answer.

Answer 35

well i feel confident in my answer

Answer 36

whops wrong equation

Answer 37

hey i'm going to go to bed

Answer 38

just make a new thread k?

Answer 39

thx alot 4 your help

Answer 40

np

Answer 41

btw how do u get achievements?

Answer 42

thats a good question
i don't see the page that tells you what you need to do in order to receive achievement awards

Answer 43

post it in the feedback section
one of the admins will tell you

Answer 44

you might have to wait a day for a reply

Answer 45

ive been here for three days and answered 100s of questions

Answer 46

and went up to lvl 13, its kinda like a game lol

Answer 47

i enjoy helping though

Answer 48

an addictive game

Answer 49

a challenge at times

Answer 50

ok off to brush my teeth

Answer 51

the easy questions aren't really worth answering though,