Multiply & Divide 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 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

What is the difference between multiplying and dividing rational expressions?

Back

Multiplying involves direct multiplication of numerators and denominators, while dividing involves multiplying by the reciprocal of the divisor.

Front

What is the importance of factoring in rational expressions?

Back

Factoring helps to identify and cancel common factors, making it easier to simplify the expression.

Front

Provide an example of multiplying two rational expressions: (2/x) * (3/y).

Back

(2/x) * (3/y) = (2*3)/(x*y) = 6/(xy).

Front

Provide an example of dividing two rational expressions: (4/x) ÷ (2/y).

Back

(4/x) ÷ (2/y) = (4/x) * (y/2) = (4y)/(2x) = (2y)/x.

Front

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

Back

(x^2 - 1)/(x + 1) = (x - 1)(x + 1)/(x + 1) = x - 1, for x ≠ -1.