Simplifying Rational Functions

Front

What is a rational function?

Back

A rational function is a function that can be expressed as the quotient of two polynomials.

Front

What does it mean to simplify a rational function?

Back

To simplify a rational function means to reduce it to its simplest form, removing any common factors in the numerator and denominator.

Front

What is the first step in simplifying a rational function?

Back

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

Front

How do you identify common factors in a rational function?

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 - 4)/(x - 2)?

Back

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

Front

What happens to the value of a rational function when you cancel a common factor?

Back

Cancelling a common factor does not change the value of the function, except at the points where the factor equals zero.

Front

What is the simplified form of (3x^2)/(6x)?

Back

The simplified form is (1/2)x.

Front

How do you simplify (n^2 - 1)/(n - 1)?

Back

Factor the numerator as (n - 1)(n + 1) and cancel the common factor to get (n + 1).

Front

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

Back

The simplified form is (1/2)p.

Front

What is the significance of identifying restrictions in rational functions?

Back

Identifying restrictions is important because it shows the values for which the function is undefined, typically where the denominator equals zero.