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

How do you divide rational expressions?

Back

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

Front

What is the first step in simplifying a rational expression?

Back

The first step is to factor both the numerator and the denominator.

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.

Front

What is a common factor in rational expressions?

Back

A common factor is a number or variable that appears in both the numerator and the denominator.

Front

What is the importance of factoring in multiplying and dividing rational expressions?

Back

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

Front

What is the result of multiplying (2x/3) * (3/4x)?

Back

The result is 1/2 after canceling the common factors.

Front

What is the result of dividing (4x^2/5) ÷ (2x/3)?

Back

The result is (12x/10) or (6x/5) after multiplying by the reciprocal.

Front

What is the restriction on the variable in rational expressions?

Back

The variable cannot make the denominator equal to zero.