\begin{tabular}{l} Subtract and simplify: \( \frac{x^{2}+14 x}{x-4}-\frac{14 x+16}{x-4} \) \\ \hline Basic Funcs Trig \end{tabular}

Hey there! Let's jump into the fun world of algebra. To subtract the two fractions, since they share a common denominator \(x - 4\), you can simply combine the numerators: \[ \frac{(x^2 + 14x) - (14x + 16)}{x - 4} \] Next, simplify that numerator: \[ x^2 + 14x - 14x - 16 = x^2 - 16 \] So now we have: \[ \frac{x^2 - 16}{x - 4} \] Recognize that \(x^2 - 16\) is a difference of squares, which can be factored as: \[ \frac{(x - 4)(x + 4)}{x - 4} \] Cancel out the \(x - 4\) terms (assuming \(x \neq 4\)), and we end up with: \[ x + 4 \] So the simplified expression is \(x + 4\). Voilà! Remember, always check for any restrictions, here \(x\) can't equal 4. Happy mathing!