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 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 the formula for multiplying two binomials?

Back

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

Front

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

Back

The LCD is found by taking the highest power of each factor present in the denominators.

Front

What is the result of dividing (x+10)/(6x+60) by (x+8)/(6x+60)?

Back

The result is (x+10)/(x+8) after canceling the common denominator.

Front

What is the significance of factoring in rational expressions?

Back

Factoring helps to simplify expressions and find common factors that can be canceled.

Front

What is the process of adding rational expressions?

Back

To add rational expressions, find a common denominator, rewrite each expression with that denominator, and then combine the numerators.

Front

What is the difference between a proper and improper rational expression?

Back

A proper rational expression has a degree of the numerator less than the degree of the denominator, while an improper one has a degree of the numerator greater than or equal to the denominator.