Question

determine the lcd of each rational expression $\frac{2y}{8xy}$ $\frac{5}{3y}$
8xy
24xy
8xy$^{2}$
24xy$^{2}$

Explanation:

Step1: Analyze denominators

The denominators are $8xy$ and $3y$.

Step2: Find LCM of coefficients

The coefficients are 8 and 3. The LCM of 8 and 3 is $8\times3 = 24$ since they are co - prime.

Step3: Find LCM of variables

For the variable $x$, it appears as $x^1$ in $8xy$ and not in $3y$, so we take $x^1$. For the variable $y$, it appears as $y^1$ in both, we take the highest power which is $y^1$.

Step4: Combine results

The LCD is the product of the LCM of coefficients and variables, so $24xy$.

Answer:

$24xy$