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 two rational expressions?

Back

To multiply two 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

What is the importance of factoring in multiplying rational expressions?

Back

Factoring helps to identify and cancel common factors, making the multiplication process easier and the final expression simpler.

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) which simplifies to (6x/5).

Front

What is the rule for multiplying rational expressions?

Back

Multiply the numerators and multiply the denominators, then simplify.

Front

What is the rule for dividing rational expressions?

Back

To divide, multiply by the reciprocal of the second expression.