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

What is the domain of a rational expression?

Back

The domain of a rational expression is all real numbers except where the denominator equals zero.

Front

How do you simplify 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 process for adding rational expressions?

Back

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

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

How do you multiply rational expressions?

Back

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

Front

How do you divide rational expressions?

Back

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

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

What is a vertical asymptote in the context of rational expressions?

Back

A vertical asymptote occurs at values of x that make the denominator zero, indicating that the function approaches infinity.

Front

What is a horizontal asymptote?

Back

A horizontal asymptote describes the behavior of a rational function as x approaches infinity or negative infinity.