Final answer:
The least common denominator (LCD) of the rational expressions 2/x + 3/x² is x². To add the expressions, multiply the first expression by x/x and the second expression by x²/x² to make the denominators the same.
Step-by-step explanation:
The least common denominator (LCD) of the rational expressions 2/x + 3/x² is x².
To find the LCD, we need to determine the lowest multiple that both denominators, x and x², have in common. In this case, x² is the least common denominator because it includes both x and x².
To add the rational expressions, we need to make the denominators the same. To do this, we multiply the first expression by x/x and the second expression by x²/x². This gives us (2x+x)/x², which simplifies to (3x)/x², and adding them together results in (2x+3x)/x² = 5x/x².