Rational Expressions & Equations

Front

What is a rational expression?

Back

A rational expression is a fraction where both the numerator and the denominator are 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 find the x-coordinate of a hole in a rational function?

Back

To find the x-coordinate of a hole, factor the numerator and denominator, and set the common factors to zero.

Front

What does it mean for a rational expression to be undefined?

Back

A rational expression is undefined when its denominator equals zero.

Front

How do you simplify a rational expression?

Back

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

Front

What is the process for adding rational expressions?

Back

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

Front

What is the formula for multiplying rational expressions?

Back

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

Front

What is the formula for dividing rational expressions?

Back

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

Front

What is a vertical asymptote in a rational function?

Back

A vertical asymptote occurs at values of x that make the denominator zero but not the numerator.