Curriculum placement
Algebra 2. This describes the skill, not a learner estimate.
Operations on rational expressions
Operate on rational expressions while retaining domain restrictions
Problem types
- Solve a rational inequality
- Simplify and keep the exclusions
- Combine rational expressions
- Choose the factored quotient of a cubic divided by a linear binomial
Builds on
- Factoring quadratic expressions
- Values a rational expression excludes
- Dividing fractions
- Dividing polynomials · Useful idea
Simplifying a rational expression divides the numerator polynomial by a factor of the denominator.
- Proving a polynomial identity · Useful idea
Identities such as the difference of squares factor a numerator or denominator so that a rational expression simplifies.
- Regions defined by inequalities · Earlier idea
A rational inequality is solved by testing signs on each side of the zeros and excluded values.
- Structure of an expression · Useful idea
Reading the structure of a numerator and denominator shows which factors cancel when simplifying.
- Simplifying complex fractions · Earlier idea
Dividing one fraction by another extends to dividing one rational expression by another.
- Greatest common factor and least common multiple · Useful idea
Adding rational expressions uses the least common multiple of the denominators, and simplifying uses the greatest common factor.
- Adding and subtracting unlike fractions · Earlier idea
Finding a common denominator to add fractions is the same step used to add rational expressions.
Leads to
- Solving rational equations
- Asymptotes, holes, and intercepts
- Permutations and combinations · See it applied
The number of combinations is a ratio of factorials that simplifies by canceling common factors.
Related skills
- Rational equations with one denominator · Shared foundations
- Solving quadratic equations · Shared foundations
Open the interactive map to explore lessons and skill connections.