Question 374927
How?
You start with a function that has {{{x/x}}} and {{{1/x^2}}} and ended it with a function that has {{{x^3/x^2}}}. 
Something is not correct.
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Use the common denominator,{{{(x-1)^2}}}.
{{{(x + 1)/(x-1)=((x+1)(x-1))/(x-1)^2}}}
{{{(x + 1)/(x-1)=(x^2-1)/(x-1)^2}}}
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{{{(x + 1)/(x-1) - 1/(x-1)^2=(x^2-1)/(x-1)^2-1/(x-1)^2}}}
{{{(x + 1)/(x-1) - 1/(x-1)^2=(x^2-1-1)/(x-1)^2}}}
{{{highlight((x + 1)/(x-1) - 1/(x-1)^2=(x^2-2)/(x-1)^2)}}}