Rational Expressions Flashcard

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 combine rational expressions with different denominators?

Back

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

Front

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

Back

A rational function is undefined where its 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 two rational expressions?

Back

1. Find a common denominator. 2. Rewrite each expression with the common denominator. 3. Add the numerators and simplify.

Front

What is the formula for dividing rational expressions?

Back

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

Front

What is the significance of excluding values from the domain of a rational function?

Back

Excluding values from the domain ensures that the function remains defined and avoids division by zero.

Front

How do you find the least common denominator (LCD) of two rational expressions?

Back

The LCD is the least common multiple of the denominators of the rational expressions.

Front

What is the first step in solving a rational equation?

Back

The first step is to identify and exclude any values that make the denominators zero.

Front

How do you express a rational expression in fully reduced form?

Back

To express a rational expression in fully reduced form, factor both the numerator and denominator and cancel any common factors.