Rational expressions and simple fractions are both important ideas in algebra, but they are quite different from each other.

1. What They Are:

   • A simple fraction is just a way to show a part of something using two numbers, like $\frac{3}{4}$.
   • A rational expression is a bit more complicated. It includes letters, called variables, along with numbers in both the top and bottom parts. For example, $\frac{x^2 - 1}{x + 2}$ is a rational expression.

2. How Complicated They Are:

   • Rational expressions can include variables, which makes them more intricate than simple fractions.
   • To simplify something like $\frac{x^2 - 1}{x + 2}$, we need to break down the top part (the numerator) into smaller pieces. This results in $\frac{(x - 1)(x + 1)}{x + 2}$.

3. Rules to Follow:

   • Rational expressions have some rules, too. For example, in $\frac{x^2 - 1}{x + 2}$, the value for $x$ cannot be $-2$. If it were, it would make the bottom part (the denominator) zero, which isn't allowed.

In short, both simple fractions and rational expressions show ratios, but rational expressions let us do a lot more with algebra!