Question

simplify the following rational function:
$f(x) = \frac{x+4}{x^2+4x}$
○ it is already simplified
○ $f(x) = \frac{x+4}{(x+4)(x+1)}$
○ $f(x) = \frac{4}{x^2+x}$
○ $f(x) = \frac{1}{x}$

Explanation:

Step1: Factor the denominator

The denominator $x^2+4x$ can be factored by extracting the common factor $x$:
$x^2+4x = x(x+4)$

Step2: Cancel common factors

The numerator is $x+4$, and the factored denominator is $x(x+4)$. We can cancel the common factor $(x+4)$ (where $x
eq -4$ to avoid division by zero):
$\frac{x+4}{x(x+4)} = \frac{1}{x}$

Answer:

$f(x)=\frac{1}{x}$