Step 1 :The function can be written in factored form as \(f(x)=\frac{4(x-3)(x-5)}{(x-5)(x-6)}\)
Step 2 :A removable discontinuity occurs when a factor in the denominator of a rational function also appears in the numerator. In this case, the factor \((x-5)\) appears in both the numerator and the denominator, so \(x=5\) is a removable discontinuity.
Step 3 :A vertical asymptote occurs when a factor in the denominator does not appear in the numerator. In this case, the factor \((x-6)\) only appears in the denominator, so \(x=6\) is a vertical asymptote.
Step 4 :As \(x\) approaches positive or negative infinity, the function behaves like the ratio of the leading coefficients of the numerator and the denominator. In this case, the leading coefficients are 4 and 1, so the function behaves like \(y=4\).
Step 5 :The location of the removable discontinuity is \(\boxed{5}\).
Step 6 :The location of the vertical asymptote is \(\boxed{6}\).
Step 7 :As \(x \rightarrow \pm \infty, f(x)\) behaves like \(\boxed{4}\).