Operations with rational expressions involve addition, subtraction, multiplication, and division of these expressions. Let's take a closer look at each operation:

Addition and Subtraction To add or subtract rational expressions, first ensure that the denominators are the same. If they aren't, find a common denominator by multiplying each term by the missing factors. Once you have the same denominator, combine the numerators and simplify the resulting expression. Example:

(3/x) + (2/x) = (3 + 2) / x = 5 / x

Multiplication To multiply rational expressions, multiply the numerators together and multiply the denominators together. Simplify the resulting expression by canceling out common factors. Example:

(2/x) * (5/x) = 10 / (x^2)

Division To divide rational expressions, invert the second expression and multiply. Example:

(2/x) / (4/x) = (2/x) * (x/4) = 2/4 = 1/2