I'm sorry for the terrible formatting, I'm sorta new so I don't know how to use MathJax very well :( see below for my first attempt :)
I came across the indical expression : $$\frac{x-1}{x-x^{1/2}-2}$$
When I first saw this expression I thought this was the final answer, however it apparently can be simplified to: $$\frac{x^{1/2}-1}{x^{1/2}-2}$$
However I struggle so see how the factorization in this equation is done as my various attempts have resulted in more complicated or wrong expressions. However I have substituted values and the answer is right. If you could please explain the factorization/steps required I would be very thankful :)