Question

\(1+\dfrac{\sqrt{\left(x-1\right)}}{x-1}\)

Answer 1

=(x-1)/(x-1) + \(\sqrt{x-1}\)/(x-1)

=\(\dfrac{x-1+\sqrt{x-1}}{x-1}\)

=\(\dfrac{\sqrt{x-1}\left(\sqrt{x-1}+1\right)}{\sqrt{\left(x-1\right)^2}}\)

=\(\dfrac{\sqrt{x-1}+1}{\sqrt{x-1}}\)

Answer 2

\(1+\dfrac{\sqrt{\left(x-1\right)}}{x-1}\)

\(=1+\dfrac{1}{\sqrt{x-1}}=\dfrac{\sqrt{x-1}+1}{\sqrt{x-1}}\)