Simplifying/Multiplying/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 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 first step in multiplying rational expressions?

Back

The first step is to factor all numerators and denominators.

Front

How do you multiply two rational expressions?

Back

Multiply the numerators together and the denominators together, then simplify if possible.

Front

What is the process for dividing rational expressions?

Back

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

Front

What does it mean to find the product of rational expressions?

Back

Finding the product means multiplying the two rational expressions together.

Front

What is a common mistake when simplifying rational expressions?

Back

A common mistake is to cancel terms that are not factors of both the numerator and denominator.

Front

What is the importance of factoring in rational expressions?

Back

Factoring is crucial because it allows for the identification and cancellation of common factors.

Front

What is the result of multiplying (2/x) by (3/x^2)?

Back

The result is (6/x^3).

Front

How do you simplify (x^2 - 1)/(x + 1)?

Back

Factor the numerator to get (x - 1)(x + 1)/(x + 1) and then cancel to get (x - 1).