Mathematics - Limits Question with Solution | TestHub

Given $f(x)=g(x)h(x)$ $\Rightarrow h(x)=\frac{f(x)}{g(x)}$ $\Rightarrow {\lim }_{x\to 1}h(x)={\lim }_{x\to 1}\frac{f(x)}{g(x)}$ $\Rightarrow {\lim }_{x\to 1}\frac{\left(x^5-1\right)\left(x^3+1\right)}{\left(x^2-1\right)\left(x^2-x+1\right)}$ $={\lim }_{x\to 1}\frac{x^5-1^5}{x-1}=5\times 1^4=5$