Multiplying and Dividing 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

What does it mean to simplify a rational expression?

Back

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

Front

What is the process for dividing rational expressions?

Back

To divide rational expressions, multiply the first expression by the reciprocal of the second expression.

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

What is the importance of checking for zero in the denominator?

Back

A denominator cannot be zero, as it would make the expression undefined. Always check for values that make the denominator zero before simplifying.

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 does it mean to factor a polynomial?

Back

Factoring a polynomial means expressing it as a product of its factors, which can help in simplifying rational expressions.

Front

What is the first step in dividing rational expressions?

Back

The first step is to factor all numerators and denominators completely.

Front

What is a common mistake when dividing rational expressions?

Back

A common mistake is forgetting to multiply by the reciprocal of the second expression.

Front

What is the result of dividing a rational expression by itself?

Back

Dividing a rational expression by itself (assuming it is not zero) results in 1.