Question 68071
You need to get rid of the denominators in the smaller individual fractions. This will make the overall expression easier to deal with.

{{{ ((1/(1-x))+(x/(x-1))) / ((1/(1-x))-(x/(x-1))) }}}

multiply by (1-x)

{{{ ((1)+(x(1-x)/(x-1))) / ((1)-(x(1-x)/(x-1))) }}}

multiply by (x-1)

{{{ ((x-1)+(x(1-x))) / ((x-1)-(x(1-x))) }}}

Now expand the brackets

{{{ ((x-1)+(x-x^2)) / ((x-1)-(x-x^2)) }}}

Simplify

{{{ (-x^2+2x-1) / (-x^2-1)}}}

If you try and simplify this any further you may find the bottom term is hard to factorise, because you will need to use the square root of a negative number