5 Questions
What is a rational expression?
The quotient of two polynomials
What is the domain of a rational expression?
The set of real numbers for which the expression is defined
How is a rational expression simplified?
If its numerator and denominator have no common factors other than 1 or -1
What must be excluded from the domain of $\frac{4x}{2x-1(x+3x-18)}$?
$x = -3$ and $x = \frac{9}{2}$
What is the product of two rational expressions?
The product of their numerators over the product of their denominators
Study Notes
Rational Expressions
- A rational expression is an expression that can be written as the quotient or ratio of two polynomials, often in the form of a fraction.
- It represents a fraction of two polynomials, such as (3x^2 + 2x - 1) / (x + 2).
Domain of a Rational Expression
- The domain of a rational expression is the set of values of the variable that make the expression valid.
- It excludes values that make the denominator zero.
Simplifying Rational Expressions
- Simplifying a rational expression involves dividing both the numerator and denominator by their greatest common divisor (GCD).
- The goal is to express the rational expression in its simplest form.
Domain of a Specific Rational Expression
- In the expression 4x / (2x - 1(x+3x-18)), the domain excludes values that make the denominator zero.
- To find the excluded values, set the denominator equal to zero and solve for x.
Product of Two Rational Expressions
- The product of two rational expressions is another rational expression.
- To multiply rational expressions, multiply the numerators and multiply the denominators, and then simplify the result.
Test your understanding of rational expressions and their domains with this quiz on College and Advanced Algebra 1.9. Explore examples of rational expressions and learn to identify the domain of these expressions to avoid division by zero.
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