Verified answer

lim(x→0) [1/(x²+x) - 1/x]

Multiply by x/x, keeping 1/x part outside the brackets:

lim(x→0) (1/x)[x/(x²+x) - x/x]

= lim(x→0) (1/x)[1/(x+1) - 1]

= lim(x→0) [1/(x+1) - 1] / x

Intederminate (0/0), apply L'Hopital's Rule:

= lim(x→0) [-1/(x+1)²] / 1

= -1

1/(x²+x) - 1/x = [1-(x+1)]/x(x+1) = -1/(x+1) so it tends to -1 as x tends to 0.