Perform the indicated operation. Note that the denominators are different. Simplify the result, if \[ \frac{4 x}{x^{2}+5 x+4}-\frac{1}{x+4} \] Answer: nelp(entering your answer)

To perform the operation \(\frac{4 x}{x^{2}+5 x+4}-\frac{1}{x+4}\), we first factor the denominator \(x^2 + 5x + 4\), which can be rewritten as \((x+4)(x+1)\). This gives us: \[ \frac{4x}{(x+4)(x+1)} - \frac{1}{x+4} \] To combine these fractions, we need a common denominator, which is \((x+4)(x+1)\). We rewrite the second fraction: \[ \frac{1}{x+4} = \frac{1 \cdot (x+1)}{(x+4)(x+1)} = \frac{x+1}{(x+4)(x+1)} \] Now we can combine the two fractions: \[ \frac{4x - (x + 1)}{(x+4)(x+1)} = \frac{4x - x - 1}{(x+4)(x+1)} = \frac{3x - 1}{(x+4)(x+1)} \] The result, thus simplified, is: \[ \frac{3x - 1}{(x+4)(x+1)} \] So, the final answer is: \[ \frac{3x - 1}{(x+4)(x+1)} \]