Question

how is adding and subtracting rational expressions similar to adding and subtracting simple fractions, and how they are different.

Answer 1

rational expressions are just glorified fractions ... you can consider a fraction to be a rational expression of constant functions. The operations are exactly the same.

Answer 2

let a(x) = 2
let b(x) = 3
let c(x) = 5
let d(x) = 1

\[\frac{a(x)}{b(x)}-\frac{c(x)}{d(x)}\]
\[\frac{2}{3}-\frac{5}{1}\]