f(x)=\\frac{2(x - 1)}{(x + 3)(x - 1)}\nidentify the vertical asymptote(s):
f(x)=\\frac{2(x - 1)}{(x + 3)(x - 1)}\nidentify the vertical asymptote(s):
Answer
Explanation:
Step1: Simplify the function
Cancel out the common factor ((x - 1)) in the numerator and denominator of (f(x)=\frac{2(x - 1)}{(x + 3)(x - 1)}). We get (f(x)=\frac{2}{x+3}), with the condition (x\neq1) (since the original function is undefined at (x = 1), but after simplification, the hole is at (x = 1) not a vertical asymptote).
Step2: Find the vertical asymptote
For a rational function (y=\frac{a}{x - h}+k) (in simplified form), the vertical asymptote is given by (x=h). For (y=\frac{2}{x + 3}=\frac{2}{x-(-3)}), using the formula (x - h=0) (where (h=-3)).
Answer:
(-3)