Operations with Rational Expressions

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 add rational expressions with different denominators?

Back

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

Front

What is the first step in simplifying a rational expression?

Back

The first step is to factor both the numerator and the denominator completely.

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 a restriction in a rational expression?

Back

A restriction is a value of the variable that makes the denominator zero, making the expression undefined.

Front

How do you find the restrictions of a rational expression?

Back

Set the denominator equal to zero and solve for the variable.

Front

Back

Front

What is the process for multiplying rational expressions?

Back

To multiply rational expressions, multiply the numerators together and the denominators together, then simplify if possible.

Front

What is the difference between a vertical asymptote and a hole in the graph of a rational function?

Back

A vertical asymptote occurs where the denominator is zero but the numerator is not, while a hole occurs where both the numerator and denominator are zero.

Front

How do you divide rational expressions?

Back

To divide rational expressions, multiply by the reciprocal of the divisor and then simplify.