Question

find f(x).

f(x) = \frac{x}{x - 19}

f(x) = \square
(type an exact answer.)

Explanation:

Step1: Apply the quotient rule

The quotient rule states that if \(f(x)=\frac{u(x)}{v(x)}\), then \(f^{\prime}(x)=\frac{u^{\prime}(x)v(x)-u(x)v^{\prime}(x)}{v(x)^{2}}\). Here \(u(x) = x\), so \(u^{\prime}(x)=1\); \(v(x)=x - 19\), so \(v^{\prime}(x)=1\).

$$
LATEXBLOCK0
$$

Step2: Simplify the numerator

$$
LATEXBLOCK1
$$

Answer:

\(\frac{-19}{(x - 19)^{2}}\)