Algebra 2, Unit 3: Rational Expressions and Equations. Key terms, formulas, and worked-example cues a high school student meets for this unit, building on prior units. Front: the term, formula name, or short problem cue. Back: the definition, formula, or solution method.
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- What is a rational expression?
- A fraction with polynomials in the numerator and denominator
- What values must be excluded from a rational expression's domain?
- Values that make the denominator equal to zero
- How do you simplify a rational expression?
- Factor the numerator and denominator, then cancel common factors
- Simplify: (x^2 - 4)/(x - 2)
- x + 2 (for x not equal to 2)
- How do you multiply two rational expressions?
- Multiply numerators together and denominators together, then simplify
- How do you divide two rational expressions?
- Multiply by the reciprocal of the divisor
- What must rational expressions share before you can add or subtract them?
- A common denominator
- What is the least common denominator (LCD) of rational expressions?
- The smallest expression divisible by each denominator
- What is a complex fraction?
- A fraction that contains another fraction in its numerator, denominator, or both
- What is a rational equation?
- An equation containing at least one rational expression
- What is the general strategy for solving a rational equation?
- Multiply every term by the LCD to eliminate denominators, then solve
- What is an extraneous solution?
- A solution obtained algebraically that does not satisfy the original equation
- Why must solutions to rational equations be checked?
- To rule out extraneous solutions that make a denominator zero
- What is a vertical asymptote of a rational function?
- A vertical line the graph approaches where the denominator equals zero
- What is a horizontal asymptote of a rational function?
- A horizontal line the graph approaches as x goes to infinity
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