4.2A Flashcardizz

Front

What is an extraneous solution?

Back

An extraneous solution is a solution that emerges from the process of solving an equation but does not satisfy the original equation.

Front

How do you check for extraneous solutions?

Back

To check for extraneous solutions, substitute the solution back into the original equation to see if it holds true.

Front

What is the least common denominator (LCD)?

Back

The least common denominator (LCD) is the smallest expression that can be used as a common denominator for a set of fractions.

Front

Back

The LCD is (x+2)(x-1).

Front

What are domain restrictions in rational functions?

Back

Domain restrictions are values that make the denominator zero, which are not allowed in the domain of the function.

Front

Back

The domain restriction is x ≠ 4.

Front

What is the process for solving rational equations?

Back

To solve rational equations, find the LCD, multiply both sides by the LCD, simplify, and solve for the variable.

Front

What does it mean to solve by using the LCD?

Back

Solving by using the LCD involves eliminating the denominators by multiplying through by the least common denominator.

Front

What is a rational equation?

Back

A rational equation is an equation that involves at least one fraction whose numerator and denominator are polynomials.

Front

How do you determine if a rational equation has no solution?

Back

A rational equation has no solution if the variable leads to a contradiction, such as a false statement.