- Just like rational numbers (which are expressed in the form of , where and are integers and ), rational expressions are simply ratios of two polynomials.
- Mathematically, a rational expression in variable '' can be represented as , in which the value of can never be zero.
- Some examples of rational expressions include: , , , etc.
- In general, simplifying any rational expression can be accomplished in two steps.
- Factorize the polynomials of the numerator and denominator
- Reduce the expression by canceling out common factors
Example 1: Is a rational expression?
Answer: No, because the numerator is not a polynomial.
Example 2: Is as rational expression?
Solution: Yes, because can be expressed as which satisfied the definition of a rational expression.
Example 3: Simplify .
Example 4: Simplify .
Example 5: Simplify .
Example 6: Simplify .
- To simplify any rational expression, factorize the polynomials in the numerator and denominator and cancel out the common factors.
- A rational expression is not defined for .