Rational Expressions

Definition

Rational expressions are algebraic expressions that represent the quotient of two polynomial functions. They are used to perform operations such as addition, subtraction, multiplication, and division with fractions that have variable numerators and denominators.

5 Must Know Facts For Your Next Test

1. Rational expressions can be added or subtracted by finding a common denominator and then adding or subtracting the numerators.
2. When adding or subtracting rational expressions with unlike denominators, the least common multiple (LCM) of the denominators is used as the common denominator.
3. Rational expressions can be multiplied by multiplying the numerators and multiplying the denominators.
4. Rational expressions can be divided by inverting the second fraction and multiplying the first fraction by the inverted second fraction.
5. Simplifying rational expressions involves factoring the numerator and denominator and canceling common factors.

Review Questions

• Explain the process of adding and subtracting rational expressions with unlike denominators.
  • To add or subtract rational expressions with unlike denominators, the first step is to find the least common multiple (LCM) of the denominators. The LCM becomes the common denominator for all the rational expressions. Then, you rewrite each rational expression with the LCM as the denominator, adjusting the numerators accordingly. Finally, you can add or subtract the numerators and write the result over the common denominator.
• Describe the steps involved in multiplying and dividing rational expressions.
  • To multiply rational expressions, you multiply the numerators together and multiply the denominators together. To divide rational expressions, you invert the second fraction and then multiply the first fraction by the inverted second fraction. This is equivalent to multiplying the first fraction by the reciprocal of the second fraction. The key is to perform the operations on the numerators and denominators separately, following the rules of exponents and factoring to simplify the resulting expression.
• Analyze the importance of simplifying rational expressions and explain the strategies used to do so.
  • Simplifying rational expressions is crucial because it reduces the expression to its most basic form, making it easier to work with and understand. The main strategy for simplifying rational expressions is to factor the numerator and denominator, and then cancel any common factors between the numerator and denominator. This process eliminates unnecessary terms and makes the expression more manageable. Simplifying rational expressions is an important skill for solving equations, inequalities, and other algebraic problems involving fractions with variables.

Related terms

Polynomial:

A polynomial is an algebraic expression that consists of variables and coefficients, with exponents that are non-negative integers.

Quotient:

The quotient is the result of dividing one number or expression by another.

Simplifying Rational Expressions: The process of reducing a rational expression to its simplest form by factoring the numerator and denominator and canceling common factors.