g) \( \lim _{x \rightarrow 0^{+}}\left(\frac{1}{x^{2}+x}-\frac{1}{x}\right) \)

Calculate the limit \( \lim _{x \rightarrow 0^{+}}\left(\frac{1}{x^{2}+x}-\frac{1}{x}\right) \). Evaluate the limit by following steps: - step0: Evaluate using transformations: \(\lim _{x\rightarrow 0^{+}}\left(\frac{1}{x^{2}+x}-\frac{1}{x}\right)\) - step1: Simplify: \(\lim _{x\rightarrow 0^{+}}\left(\frac{-1}{x+1}\right)\) - step2: Reduce the fraction: \(\lim _{x\rightarrow 0^{+}}\left(-\frac{1}{x+1}\right)\) - step3: Rewrite the expression: \(\frac{\lim _{x\rightarrow 0^{+}}\left(-1\right)}{\lim _{x\rightarrow 0^{+}}\left(x+1\right)}\) - step4: Evaluate: \(\frac{-1}{\lim _{x\rightarrow 0^{+}}\left(x+1\right)}\) - step5: Evaluate: \(\frac{-1}{1}\) - step6: Divide the terms: \(-1\) The limit of \( \frac{1}{x^{2}+x}-\frac{1}{x} \) as \( x \) approaches 0 from the right is -1.