I read ((x^4 - x^3) / x^4 + x^3) * ((x+1)-2x(1+x))/ x-1 as ((x^4 - x^3) / x^4 + x^3) * ((x+1)-2x(1+x))/(x-1).
First simplify the last part of the expression: (1-2x)(1+x)/(x-1).
x^4-x^3=x^3(x-1) and x^4+x^3=x^3(x+1) so the first part of the expression is (x-1)/(x+1).
Now we can simplify the whole expression: (x-1)/(x+1)*(1-2x)(1+x)/(x-1) = 1-2x. (Strike through indicates cancellation.)