A rational expression is an algebraic expression that contains one or more fractions with variables in the numerator and/or denominator. It can be simplified by factoring out common factors and canceling out common terms in the numerator and denominator.
To simplify a rational expression, first factor the numerator and denominator completely. Then, cancel out any common factors in the numerator and denominator. If there are no common factors, multiply the numerator and denominator by the conjugate of the denominator to eliminate any complex or irrational terms.
Simplifying a rational expression involves reducing it to its simplest form by canceling out common factors. Solving a rational expression, on the other hand, involves finding the value of the variable that makes the expression equal to a specific number.
No, a rational expression cannot have a zero denominator. This would result in an undefined expression since division by zero is undefined in mathematics.
Some common mistakes to avoid when simplifying rational expressions include forgetting to factor completely, canceling out terms incorrectly, and forgetting to check for extraneous solutions. It is important to carefully follow the steps of simplifying and always check the final expression for any errors.