Identify the given rational expression: \(\frac{12}{x+3}\).
Substitute the given value \(x = -1\) into the expression, replacing every \(x\) with \(-1\).
Rewrite the expression after substitution as \(\frac{12}{-1 + 3}\).
Simplify the denominator by performing the addition inside the denominator: calculate \(-1 + 3\).
Express the simplified rational expression as \(\frac{12}{\text{(result from previous step)}}\) and note that this is the value of the expression at \(x = -1\).