Question

determine the lcd of each rational expression $\frac{x - 4}{x + 5}$ $\frac{x}{2x + 10}$
$x + 5$
$2x + 5$
$2x + 10$
$3x + 15$

Explanation:

Step1: Factor the denominators

The first denominator is $x + 5$. The second denominator $2x+10$ can be factored as $2(x + 5)$ since $2x+10=2\times x+2\times5 = 2(x + 5)$.

Step2: Determine the LCD

The least - common denominator is the product of all unique factors, each raised to the highest power to which it occurs in any of the factorizations. Here, the factors are $2$ and $(x + 5)$. The highest power of $2$ is $2^1$ and the highest power of $(x + 5)$ is $(x + 5)^1$. So the LCD is $2(x + 5)=2x+10$.

Answer:

$2x + 10$