Question

4
select the correct answer.
what is the least common denominator that can be used to solve this equation?
\\(\frac{1}{x} + \frac{3}{x - 3} = 5\\)
a. \\(x - 3\\)
b. \\(x\\)
c. \\(5x(x - 3)\\)
d. \\(x(x - 3)\\)

Explanation:

Step1: Identify denominators

The equation is $\frac{1}{x} + \frac{3}{x - 3} = 5$. The denominators are $x$ and $x - 3$.

Step2: Find least common denominator (LCD)

The LCD of two rational expressions with denominators $x$ and $x - 3$ (which are distinct linear factors) is the product of the denominators. So, the LCD is $x(x - 3)$.

Answer:

D. $x(x - 3)$