what is the meaning term rational expression Please give me an example how to divide rational expressions

Since this is not my area of expertise, I searched Google under the key words "rational expressions" to get this possible source:

http://tutorial.math.lamar.edu/Classes/Alg/RationalExpressions.aspx

In the future, you can find the information you desire more quickly, if you use appropriate key words to do your own search. Also see http://hanlib.sou.edu/searchtools/.

A rational expression is a fraction where both the numerator and denominator are polynomials. It represents a ratio of two polynomial expressions. Rational expressions are commonly used in algebraic equations and functions.

To divide rational expressions, you can follow these steps:

Step 1: Simplify the expressions if possible by factoring the numerator and denominator.

Step 2: Take the reciprocal of the second rational expression that you want to divide by. This means swapping the numerator and denominator of the expression.

Step 3: Multiply the first rational expression (dividend) by the reciprocal of the second rational expression (divisor).

Step 4: Simplify the resulting expression, if necessary, by canceling out common factors.

Here's an example of how to divide rational expressions:

Divide (x^2 + 3x - 4) / (x - 1) by (x + 1) / (x - 2).

Step 1: Factor the expressions (if possible):
Numerator: x^2 + 3x - 4 = (x + 4)(x - 1)
Denominator: x - 1 (already factored)
Divisor: x + 1 (already factored)
No further simplification is needed here.

Step 2: Take the reciprocal of the divisor:
Reciprocal of (x + 1) / (x - 2) is (x - 2) / (x + 1)

Step 3: Multiply the first rational expression by the reciprocal of the second expression:
[(x + 4)(x - 1)] * [(x - 2) / (x + 1)]

Step 4: Simplify the expression:
[(x + 4)(x - 1)] * [(x - 2) / (x + 1)] = (x + 4)(x - 2)

Therefore, the division of the given rational expressions is (x + 4)(x - 2).