AA C&C Unit 7 FLASHCARD 2: Add/Sub & Solve Rational Equations

Front

What is a rational expression?

Back

A rational expression is a fraction where both the numerator and the denominator are polynomials.

Front

How do you find the least common denominator (LCD) of two rational expressions?

Back

To find the LCD, factor each denominator into its prime factors and take the highest power of each factor.

Front

What is the process of adding rational expressions?

Back

To add rational expressions, find a common denominator, rewrite each expression with the common denominator, and then combine the numerators.

Front

What is the difference between a proper and improper rational expression?

Back

A proper rational expression has a degree in the numerator that is less than the degree in the denominator, while an improper rational expression has a degree in the numerator that is greater than or equal to the degree in the denominator.

Front

What does it mean to simplify a rational expression?

Back

Simplifying a rational expression means reducing it to its lowest terms by canceling common factors in the numerator and denominator.

Front

How do you solve a rational equation?

Back

To solve a rational equation, find a common denominator, eliminate the denominators by multiplying both sides by the LCD, and then solve the resulting equation.

Front

What is the importance of checking for extraneous solutions in rational equations?

Back

Checking for extraneous solutions is important because multiplying by the LCD can introduce solutions that do not satisfy the original equation.

Front

What is the formula for finding the quotient of two rational expressions?

Back

To find the quotient of two rational expressions, multiply the first expression by the reciprocal of the second expression.

Front

What is factoring in the context of rational expressions?

Back

Factoring involves rewriting a polynomial as a product of its factors, which can help simplify rational expressions.

Front

What is the significance of the common denominator in adding or subtracting rational expressions?

Back

The common denominator allows you to combine the numerators of the rational expressions accurately.