Simplify Rational Expressions Scheerhorn

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 simplify a rational expression?

Back

To simplify a rational expression, factor both the numerator and the denominator and then cancel any common factors.

Front

What does it mean to factor a polynomial?

Back

Factoring a polynomial means expressing it as a product of its factors, which are polynomials of lower degrees.

Front

What is the first step in simplifying the expression (n^2 - 7n + 12)/(n - 3)?

Back

The first step is to factor the numerator, which can be factored as (n - 3)(n - 4).

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 identifying restrictions in rational expressions?

Back

Identifying restrictions is important because it helps to determine values that would make the denominator zero, which are not allowed.

Front

What is a common mistake when simplifying rational expressions?

Back

A common mistake is to cancel terms that are not factors of both the numerator and the denominator.

Front

How do you handle complex fractions?

Back

To simplify complex fractions, rewrite them as a single fraction by finding a common denominator.

Front

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

Back

The simplified form is 1/(2x) after canceling the common factor of 2x.

Front

What does it mean to have a removable discontinuity in a rational expression?

Back

A removable discontinuity occurs when a factor cancels out, indicating a hole in the graph of the function.