Question 179377
I assume that you want to evaluate the limit as x approaches -1


{{{lim(x->-1,(x^2+x)/(x+1))}}} Start with the given limit



{{{lim(x->-1,(x(x+1))/(x+1))}}} Factor out the GCF x



{{{lim(x->-1,(x*cross((x+1)))/cross((x+1)))}}} Cancel out like terms



{{{lim(x->-1,(x))}}} Simplify



{{{-1}}} Take the limit of x as x approaches -1. In other words, simply plug in x=-1



So {{{lim(x->-1,(x^2+x)/(x+1))=-1}}}



Note: If you use a calculator to make the table of {{{f(x)=(x^2+x)/(x+1)}}}, you'll see that {{{x=-1}}} is NOT defined, but {{{f(x)}}} values near that value get close to -1.