Question: Find the least common denominator of $\frac{7}{x-4}$ and $\frac{5}{x+4}$.

Find the least common denominator of $\frac{7}{x-4}$ and $\frac{5}{x+4}$.

Solution

To find the least common denominator (LCD) of the fractions \[ \frac{7}{x-4} \quad \text{and} \quad \frac{5}{x+4}, \] we need to determine the least common multiple of the denominators. The denominators are \(x-4\) and \(x+4\). Since these are two distinct linear factors, their least common multiple is simply their product: \[ (x-4)(x+4). \] Therefore, the least common denominator is \[ x^2 - 16. \]