Find the least common denominator of \( \frac{-5}{4 x+12} \) and \( \frac{x}{x+3} \). ■

To find the least common denominator (LCD) of the fractions \(\frac{-5}{4x+12}\) and \(\frac{x}{x+3}\), we first need to factor the denominators. The first denominator, \(4x + 12\), can be factored as: \[ 4x + 12 = 4(x + 3) \] The second denominator, \(x + 3\), is already in its simplest form. Now, the denominators we have are \(4(x + 3)\) and \(x + 3\). To find the LCD, we take the highest power of each factor that appears in any of the denominators. The factor \(4\) comes from the first denominator, and the factor \((x + 3)\) appears in both. Thus, the least common denominator is: \[ LCD = 4(x + 3) \] This is the least common denominator that can be used to combine the two fractions into a single fraction.