4-3 Simplify, Multiply, and Divide 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

What does it mean to simplify a rational expression?

Back

To simplify a rational expression means to reduce it to its lowest terms by canceling common factors in the numerator and denominator.

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 domain restriction in rational expressions?

Back

The domain restriction refers to the values of the variable that make the denominator zero, which are not allowed in the expression.

Front

How do you find the domain of a rational expression?

Back

To find the domain, set the denominator equal to zero and solve for the variable; the solutions are the restrictions.

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 does it mean to divide rational expressions?

Back

Dividing rational expressions involves multiplying by the reciprocal of the divisor.

Front

How do you divide (x+2)/(x+3) by (x+4)/(x+5)?

Back

To divide, multiply (x+2)/(x+3) by the reciprocal of (x+4)/(x+5), resulting in (x+2)(x+5)/((x+3)(x+4)).

Front

What is the first step in simplifying a complex rational expression?

Back

The first step is to factor the numerator and denominator where possible.

Front

What is the significance of canceling common factors in rational expressions?

Back

Canceling common factors simplifies the expression and helps to find the simplest form.