Simplifying 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

What does it mean to simplify a rational expression?

Back

To simplify a rational expression means to reduce it to its simplest form, where the numerator and denominator have no common factors other than 1.

Front

What is the first step in simplifying a rational expression?

Back

The first step is to factor both the numerator and the denominator completely.

Front

How do you identify common factors in a rational expression?

Back

Common factors can be identified by factoring both the numerator and denominator and looking for identical factors.

Front

What is the result of simplifying (x^2 - 9)/(x + 3)?

Back

The result is (x - 3) after factoring the numerator as (x + 3)(x - 3) and canceling the common factor.

Front

What is the importance of checking for restrictions in rational expressions?

Back

Restrictions are important because they indicate values that would make the denominator zero, which are not allowed in rational expressions.

Front

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

Back

The simplified form is (x - 2) after factoring the numerator as (x + 2)(x - 2) and canceling the common factor.

Front

How do you simplify the expression (2x^2)/(4x)?

Back

The simplified expression is (x/2) after dividing both the numerator and denominator by 2x.

Front

What is the simplified form of (x^2 + 5x + 6)/(x + 2)?

Back

The simplified form is (x + 3) after factoring the numerator as (x + 2)(x + 3) and canceling the common factor.

Front

What does it mean if a rational expression cannot be simplified?

Back

It means that the numerator and denominator have no common factors other than 1.