Question

adding and subtracting rational expressions
rewriting a sum of rational expressions using a common denominator
what is the least common denominator (lcd) of the rational expressions being added?
\\(\frac{2}{x} + \frac{3}{x^2}\\)
options: (x^2), (x^3), (x)

Explanation:

Step1: Identify denominators

The denominators of the rational expressions $\frac{2}{x}$ and $\frac{3}{x^2}$ are $x$ (which is $x^1$) and $x^2$.

Step2: Determine LCD of exponents

To find the least common denominator (LCD) of the powers of $x$, we take the highest power of $x$ present. The powers are $x^1$ and $x^2$. The highest power is $x^2$. So the LCD of $x$ and $x^2$ is $x^2$.

Answer:

$x^2$ (corresponding to the first option with text $x^2$)