simplifying

I don't understand how they simplified the expression to get the x value.

I've tried squaring the expression to get rid of the square roots but am not getting anything close to what I'm supposed to get.

As you say, theyve just squared both sides, so maybe post what you tried?

This is how I did the question

You need to square the full left hand side so
(a + b)^2 = a^2 + b^2 + 2ab
Youre missing the 2ab term.

But i thought if you squared the square root of some terms, you would just get those terms?

You do, those are the a^2 and the b^2 terms. Youre missing the 2ab term.

To be a bit more explicit on the left you have
sqrt(x^2+1) - 2sqrt(x^2-1)
So a+b. Squaring the full expression, so (a+b)^2, you get
(sqrt(x^2+1))^2 + (-2sqrt(x^2-1))^2 + 2(sqrt(x^2+1))(-2sqrt(x^2-1))
You missed out the 2ab term

thanks