Question 277509
{{{(x^(-1)+2x^(-2))/(1+x^(-1))}}} Start with the given expression.



{{{(1/x+2/(x^2))/(1+1/x)}}} Rewrite sub expression with positive exponents (just flip the base)



{{{(x^(cross(2))(1/cross(x))+cross(x^2)(2/cross(x^2)))/(x^2+x^(cross(2))(1/cross(x)))}}} Multiply EVERY term by the inner LCD {{{x^2}}} to clear out the inner fractions.



{{{(x+2)/(x^2+x)}}} Simplify



So {{{(x^(-1)+2x^(-2))/(1+x^(-1))=(x+2)/(x^2+x)}}} which is equivalent to what you have (you just have the denominator factored)