Question

\(\lim\limits_{x\rightarrow1}\dfrac{-x^4-5x+6}{x^2+5x-6}\)

Answer 1

\(\lim\limits_{x\rightarrow1}\dfrac{-x^4-5x+6}{x^2+5x-6}=\lim\limits_{x\rightarrow1}\dfrac{-\left(x-1\right)\left(x^3+x^2+x+6\right)}{\left(x-1\right)\left(x+6\right)}\)

\(=\lim\limits_{x\rightarrow1}\dfrac{-\left(x^3+x^2+x+6\right)}{x+6}=\dfrac{-9}{7}\)