Question

lim (1 / x^2 + x)-(1/x)
x -> 0

Answer 1

$obs: \frac{a}{b} - \frac{c}{d} = \frac{a.d - b.c}{b.d}$

$( \frac{1}{x {}^{2} + x} ) - ( \frac{1}{x} ) \\ \\ \frac{x - (x {}^{2} + x)}{x.(x {}^{2} + x)} = \frac{x - x {}^{2} - x}{x {}^{3} + x {}^{2} }$

$\frac{ - x {}^{2} }{x {}^{3} + x {}^{2} } = \frac{x. ( - x)}{x.(x {}^{2} + x) } = \frac{ - x}{x {}^{2} + x}$

$\frac{ -1.x}{x.(x + 1)} = \frac{ - 1}{(x + 1)} = \frac{ - 1}{0 + 1} = \frac{ - 1}{1} = - 1$

Acho que deu pra entender :v