Operations with Rational Expressions

Front

What is a restriction in rational expressions?

Back

A value of a variable that makes the expression mathematically illegal.

Front

How do we find the restrictions of a rational expression?

Back

We set the denominator equal to zero and solve for the variable.

Front

What is a rational expression?

Back

A fraction where the numerator and the denominator are both polynomials.

Front

What is the first step in simplifying a rational expression?

Back

Factor both the numerator and the denominator.

Front

What does it mean to simplify a rational expression?

Back

To reduce it to its lowest terms by canceling common factors.

Front

What is a vertical asymptote?

Back

A line that a graph approaches but never touches, occurring where the denominator is zero.

Front

What is a hole in the graph of a rational expression?

Back

A point where the function is undefined due to a common factor in the numerator and denominator.

Front

What is the difference between a restriction and a vertical asymptote?

Back

A restriction is a value that makes the expression undefined, while a vertical asymptote is a line that the graph approaches.

Front

How do you determine if a rational expression is undefined?

Back

By checking if the denominator equals zero for any value of the variable.

Front

What is the process of adding rational expressions?

Back

Find a common denominator, rewrite each expression, and then combine the numerators.