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

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 term that appears in both the numerator and the denominator of a rational expression.

Front

How do you identify restrictions in rational expressions?

Back

Restrictions are found by setting the denominator equal to zero and solving for the variable.

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 + 1)?

Back

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

Front

What is the simplified form of (x^2 - 4)/(x^2 - 2x)?

Back

The simplified form is (x + 2)/(x) after factoring and canceling.

Front

What is the formula for multiplying two binomials?

Back

The formula is (a + b)(c + d) = ac + ad + bc + bd.