Question: Finding the LCD of rational expressions with linear denominators:… Find the least common…

Finding the LCD of rational expressions with linear denominators:…

Find the least common denominator of $\frac{7}{8x}$ and $\frac{2}{7x+3}$.

Solution

To find the least common denominator (LCD) of the rational expressions \(\frac{7}{8x}\) and \(\frac{2}{7x+3}\), we need to determine the least common multiple of the denominators \(8x\) and \(7x+3\). Step 1: Identify the denominators of each expression. - The first denominator: \(8x\) - The second denominator: \(7x+3\) Step 2: Since the denominators are already linear and distinct, the LCD is simply the product of these denominators: \[ 8x(7x+3) \] Thus, the least common denominator is \(8x(7x+3)\).