Select the correct answer.What is the least common denominator that can be used to solve this equation?1𝑥+2𝑥−3=5 A. 5⁢𝑥⁢(𝑥−3) B. 𝑥 C. 𝑥⁢(𝑥−3) D. 𝑥−3

To find the least common denominator (LCD) that can be used to solve the equation $\frac{1}{x} + \frac{2}{x-3} = 5$, follow these steps:

1. Identify the denominators: The denominators in the equation are $x$ and $x-3$.

2. Find the least common denominator (LCD): The LCD is the smallest expression that both denominators can divide into without leaving a remainder. For $x$ and $x-3$, the LCD is the product of these two distinct linear factors, since they have no common factors other than 1.

   Therefore, the LCD is $x(x-3)$.

3. Select the correct answer: From the given options:

   • A. $5x(x-3)$
   • B. $x$
   • C. $x(x-3)$
   • D. $x-3$

   The correct answer is C. $x(x-3)$.

So, the least common denominator that can be used to solve the equation is $x(x-3)$.