Multiplying and Dividing 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

How do you multiply rational expressions?

Back

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

Front

What is the first step in dividing rational expressions?

Back

The first step is to multiply by the reciprocal of the divisor.

Front

What does it mean to simplify a rational expression?

Back

Simplifying a rational expression means reducing it to its lowest terms by canceling common factors in the numerator and denominator.

Front

What is a common factor in rational expressions?

Back

A common factor is a number or variable that divides both the numerator and the denominator without leaving a remainder.

Front

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

Back

The least common denominator is the smallest expression that can be used as a denominator for all rational expressions involved.

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 difference between multiplying and dividing rational expressions?

Back

Multiplying involves combining numerators and denominators directly, while dividing requires multiplying by the reciprocal of the divisor.

Front

What is the importance of factoring in rational expressions?

Back

Factoring helps to identify and cancel common factors, making it easier to simplify the expression.

Front

What is an example of a rational expression?

Back

An example of a rational expression is (x^2 - 1)/(x + 1).