Rational Expressions Flashcards

Grade 10 · Math · Flashcards

Master the vocabulary and procedures for working with rational (algebraic fraction) expressions.

Flashcards

Rational expression: A fraction whose numerator and denominator are both polynomials
Domain restriction: Any x-value that makes the denominator equal zero; must be excluded
Simplifying rational expressions: Factor completely, then cancel identical factors in numerator and denominator
Multiplying rational expressions: Multiply numerators together and denominators together, then simplify
Dividing rational expressions: Multiply the first expression by the reciprocal of the second, then simplify
Adding rational expressions (same denominator): Add the numerators; keep the denominator the same
Adding rational expressions (different denominators): Find the LCD, rewrite each fraction, then add numerators
Least Common Denominator (LCD): The smallest polynomial divisible by all denominators in the problem
Reciprocal of a rational expression: Swap numerator and denominator; used in division
Can you cancel terms in rational expressions?: No — you can only cancel common factors, not individual terms being added
Why can't the denominator equal zero?: Division by zero is undefined in mathematics
Complex rational expression: A rational expression with fractions in the numerator or denominator; simplify by multiplying by the LCD
Extraneous solution: A solution found algebraically that must be rejected because it creates a zero denominator