Simplify, Multiply, and Divide Rational Expressions

Front

What is a rational expression?

Back

A rational expression is a fraction where both the numerator and the denominator are polynomials.

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 multiplying rational expressions?

Back

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

Front

What is the process for dividing rational expressions?

Back

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

Front

What is the reciprocal of a rational expression?

Back

The reciprocal of a rational expression is obtained by flipping the numerator and denominator.

Front

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

Back

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

Front

What is the importance of factoring in simplifying rational expressions?

Back

Factoring allows you to identify and cancel common factors, which simplifies the expression.

Front

What are excluded values in rational expressions?

Back

Excluded values are values of the variable that make the denominator zero, which are not allowed in rational expressions.

Front

How do you add or subtract rational expressions?

Back

To add or subtract rational expressions, first find a common denominator, then combine the numerators.

Front

What is the difference between proper and improper rational expressions?

Back

A proper rational expression has a degree of the numerator less than the degree of the denominator; an improper one has a degree of the numerator greater than or equal to the denominator.