Lesson R.5: Rational Expressions

Vocabulary practice flashcards covering rational expressions, domain restrictions, multiplication, division, finding the LCD, and simplifying complex fractions based on Lesson R.5.

Rational Expression

The quotient of two polynomials, which must have a variable in the denominator.

Domain of a Rational Expression

The set of all numbers that make the fraction undefined, requiring that the denominator $\neq 0$.

Multiplication of Rational Expressions

For fractions $\frac{a}{b}$ and $\frac{c}{d}$ where $b \neq 0$ and $d \neq 0$, multiply straight across to get $\frac{ac}{bd}$.

Division of Rational Expressions

For fractions $\frac{a}{b}$ and $\frac{c}{d}$ where $b \neq 0$ and $d \neq 0$, multiply by the reciprocal to get $\frac{a}{b} \cdot \frac{d}{c} = \frac{ad}{bc}$.

Steps to Find the Least Common Denominator (LCD)

1. Factor all denominators. 2. Working from left to right, write each factor (if more than one in the same denominator, write twice). 3. Multiply what is 'missing' from the original denominator on top and bottom.

Complex Fraction

The quotient of two rational expressions, or fractions within fractions.

Simplifying Complex Fractions with Fractional Binomials

Find the LCD for the original numerator and denominator separately to reduce each into one term before dividing.