Introduction
- 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.
Simplifying Rational Expressions
- 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
Solved Examples
Example 1: Is
Answer: No, because the numerator is not a polynomial.
Example 2: Is
Solution: Yes, because
Example 3: Simplify
Solution:
Example 4: Simplify
Solution:
Example 5: Simplify
Solution:
Example 6: Simplify
Solution:
Cheat Sheet
- To simplify any rational expression, factorize the polynomials in the numerator and denominator and cancel out the common factors.
- Abhishek Tiwari
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