Could someone please help me simply this expression?

[vapid igloo]

I have gotten to the part: (x+sqrt(x²-1))+(1/(x+sqrt(x²-1))) / 2

I need help proceeding from there to end up with just x

[vapid igloo]

<@&286206848099549185>

[karmic fossil]

this looks similar to hyperbolic functions
try comparing it

[vapid igloo]

I need to perform algebra to end up with simply x

Do u know what that algebra is?

[junior wagon]

hi! can someone help me translate mathematical sentences

[vapid igloo]

u r in the wrong channel, create your own post

[karmic fossil]

alright I would take a better look

[karmic fossil]

how complicated is it? send it

[vapid igloo]

What do u mean?

I have simplified it down to

(x+sqrt(x²-1))+(1/(x+sqrt(x²-1))) / 2

i need to just simpify it further but am not so sure how

[junior wagon]

Okay THANK YOU!

Wait!

Three times the smallest of three consecutive even integers is two more than twice the largest.

[finite nacelle]

to combine the terms in the numerator, i might try cross multiplying

[finite nacelle]

like MP said, please make your own post or use a help channel- this topic is being used for someone else's problem and it's kind of rude to butt in like that. Please see #❓how-to-get-help

[vapid igloo]

There are a lot of steps to end up simplifying this down to just x. Would you say that I need to show all of them or would showing a few important intermediate steps and explain that they were reached via expanding be sufficient enough?

[karmic fossil]

Alright, I did it and I got x. All you have to do is take the lcm of the numerator then simplify.

[vapid igloo]

How many simplification steps did u have?

[karmic fossil]

you need to show all of them

[vapid igloo]

Aren't there like more than 10?

[karmic fossil]

no, it is less than 5

[vapid igloo]

bruh

Can I see the steps you did?

After this line: (x+sqrt(x²-1))+(1/(x+sqrt(x²-1))) / 2, you got to x in less than 5 steps?

@karmic fossil

[karmic fossil]

I sent a picture already, my service is poor. Be patient.

[vapid igloo]

in the last line, the common factor that cancels out is just x + sqrt(x^2 - 1) right? leaving us with just x?

[karmic fossil]

Yes

Glad you understand. Now try it yourself.

[vapid igloo]

Ok I will try myself and compare to ur answer

[karmic fossil]

Very well

[vapid igloo]

ok nice

I got it!

Thank you so much! I really appreciate the help!

[karmic fossil]

You are welcome

[vast crow]

.solved