next, cancel common factors.\n lim_{x \to 4} \frac{x(x - 4)}{(x - 4)(x + 1)}=lim_{x \to 4}\frac{x}{square}
next, cancel common factors.\n lim_{x \to 4} \frac{x(x - 4)}{(x - 4)(x + 1)}=lim_{x \to 4}\frac{x}{square}
Answer
Explanation:
Step1: Cancel common factor
Cancel out the common factor $(x - 4)$ in the numerator and denominator of the fraction $\frac{x(x - 4)}{(x - 4)(x + 1)}$. $\lim_{x\rightarrow4}\frac{x(x - 4)}{(x - 4)(x + 1)}=\lim_{x\rightarrow4}\frac{x}{x + 1}$
Step2: Substitute $x = 4$
Substitute $x = 4$ into the function $\frac{x}{x+1}$. $\lim_{x\rightarrow4}\frac{x}{x + 1}=\frac{4}{4 + 1}=\frac{4}{5}$
Answer:
$\frac{4}{5}$