11/20 Rational Expressions, Equations and Inequalities

Front

What are rational expressions?

Back

Rational expressions are fractions where the numerator and the denominator are both polynomials.

Front

What is the domain of a rational expression?

Back

The domain of a rational expression is the set of all real numbers except those that make the denominator equal to zero.

Front

How do you find the vertical asymptotes of a rational function?

Back

Vertical asymptotes occur at the values of x that make the denominator zero, provided that these values do not also make the numerator zero.

Front

What is the process for simplifying a rational expression?

Back

To simplify a rational expression, factor both the numerator and the denominator and then cancel any common factors.

Front

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

Back

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

Front

How do you add or subtract rational expressions with the same denominator?

Back

To add or subtract rational expressions with the same denominator, combine the numerators and keep the common denominator.

Front

How do you add or subtract rational expressions with different denominators?

Back

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

Front

What is a complex fraction?

Back

A complex fraction is a fraction where the numerator, the denominator, or both contain fractions.

Front

How do you solve a rational equation?

Back

To solve a rational equation, find a common denominator, eliminate the fractions, and then solve the resulting equation.

Front

What is the significance of extraneous solutions in rational equations?

Back

Extraneous solutions are solutions that do not satisfy the original equation, often arising from the process of eliminating denominators.