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The concept of rational expressions, including their definition, simplification using the cancellation property and long division, multiplication and division, adding and subtracting, complex fractions, and expressions with negative exponents. It also includes examples and practice problems.
Typology: Study notes
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Lecture 4: Section A. Rational Expressions
Def. A rational expression is the quotient of two polynomials. The domain of an expression is the set of real numbers for which the expression is defined.
ex. Find the domain.
Simplifying Rational Expressions
A fraction is in simplest form if its numerator and denominator have no common factors.
Use the Cancellation Property:
if 푐 ∕= 0
ex. Simplify:
and find its domain.
Domain:
Multiplying and Dividing Rational Expressions
Recall:
Adding and Subtracting Rational Expressions
Least Common Denominator (LCD) is the least common multiple (LCM) of the denominators. To find it:
To add or subtract, write each rational expression with LCD as its denominator, and use 푎 푏
ex. Perform the operations and simplify:
Complex Fractions
Def. A complex fraction is a quotient containing rational expressions.
Method 2. Multiply numerator and denominator by the LCM of all denominators.
ex. Simplify: 1)
Expressions with Negative Exponents
Factor out the common factor with smaller exponent.
NOTE: When factoring, you subtract the exponents.
For example: 2푥−^5 /^3 − 3 푥−^2 /^3 =
ex. Write
as a single quotient without negative exponents.
Factor (푥 + 1)−^1 − (푥 + 1)−^3 (푥 + 4) completely without negative exponents.
Write
as a single quotient without negative exponents.
