Find the least common denominator of ﻿fraction numerator x plus begin display style 2 over x squared end style over denominator 3 minus begin display style 5 over x end style end fraction﻿.

To find the least common denominator (LCD) of the given expression:

\[
\frac{x + \frac{2}{x^2}}{3 - \frac{5}{x}}
\]

we need to determine the least common multiple (LCM) of the denominators within the expression.

### Step 1: Identify the denominators
- The expression inside the numerator \( x + \frac{2}{x^2} \) has the denominators \( 1 \) and \( x^2 \).
- The expression inside the denominator \( 3 - \frac{5}{x} \) has the denominators \( 1 \) and \( x \).

### Step 2: Determine the Least Common Denominator
The denominators to consider are \( x^2 \) and \( x \). 

The least common denominator (LCD) is the least common multiple (LCM) of \( x^2 \) and \( x \).

- The LCM of \( x^2 \) and \( x \) is \( x^2 \).

### Final Answer:
The least common denominator of the given expression is \( x^2 \).

Would you like more details on how this was determined or have any other questions?

Here are some related questions you might find useful:
1. How do you find the LCM of two algebraic expressions?
2. Can you simplify the given expression using the least common denominator?
3. What are the steps to solve complex fractions?
4. How do you multiply and divide algebraic fractions?
5. What is the difference between LCM and GCD in algebraic contexts?

**Tip:** When dealing with algebraic fractions, always factor the expressions to find the least common denominator more easily.

Learn how to find the least common denominator (LCD) of a fraction with algebraic expressions. Step-by-step solution to determine the LCD involving algebraic fractions. Suitable for students in Grades 9-12.

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