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?

Back

A common factor is a number or expression that divides two or more numbers or expressions evenly.

Front

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

Back

The least common denominator is the smallest expression that is a multiple of the denominators of the rational expressions.

Front

What is the result of multiplying (x + 2)/(x + 3) by (x + 4)/(x + 5)?

Back

The result is (x + 2)(x + 4) / ((x + 3)(x + 5)).

Front

What is the result of dividing (x^2 - 1)/(x + 1) by (x - 1)/(x + 2)?

Back

The result is (x^2 - 1)(x + 2) / (x - 1)(x + 1).

Front

What is the importance of factoring in simplifying rational expressions?

Back

Factoring helps identify and cancel common factors in the numerator and denominator, simplifying the expression.

Front

What does it mean to have a restriction in a rational expression?

Back

A restriction is a value that makes the denominator zero, which is not allowed in rational expressions.