Rational Expressions and Equations

Front

What is a rational expression?

Back

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

Front

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

Back

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

Front

What is the process for subtracting rational expressions?

Back

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

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

What is the first step in solving a rational equation?

Back

The first step is to find a common denominator and eliminate the fractions by multiplying both sides of the equation by that denominator.

Front

What is a polynomial?

Back

A polynomial is an algebraic expression that consists of variables raised to non-negative integer powers and coefficients.

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 variable in rational expressions?

Back

The variable can affect the domain of the expression, as certain values may make the denominator zero, leading to undefined expressions.

Front

How do you determine the domain of a rational expression?

Back

The domain is determined by identifying values of the variable that make the denominator zero and excluding them from the set of possible values.

Front

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

Back

A proper rational expression has a numerator of lower degree than the denominator, while an improper rational expression has a numerator of equal or higher degree.