Operations with 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 add rational expressions with different denominators?

Back

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

Front

What is the least common denominator (LCD)?

Back

The least common denominator (LCD) is the smallest expression that can be used as a common denominator for a set of rational expressions.

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 subtracting rational expressions?

Back

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

Front

What does it mean to multiply rational expressions?

Back

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

Front

What is the rule for dividing rational expressions?

Back

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

Front

How do you find the domain of a rational expression?

Back

The domain of a rational expression includes all real numbers except those that make the denominator equal to zero.

Front

What is a polynomial?

Back

A polynomial is an expression consisting of variables raised to non-negative integer powers and coefficients.

Front

What is the difference between a proper and improper rational expression?

Back

A proper rational expression has a degree in the numerator that is less than the degree in the denominator, while an improper rational expression has a degree in the numerator that is greater than or equal to the degree in the denominator.