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

How do you factor a polynomial?

Back

Factoring a polynomial involves expressing it as a product of its factors, which can be numbers, variables, or both.

Front

What is the first step in simplifying the expression (2p^2)/(4p)?

Back

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

Front

Simplify: (2p^2)/(4p)

Back

p/2

Front

What is the importance of identifying common factors in rational expressions?

Back

Identifying common factors allows you to cancel them out, simplifying the expression.

Front

Simplify: (x^2 - 81)/(x + 9)

Back

x - 9

Front

What is the difference between a proper and improper rational expression?

Back

A proper rational expression has a degree of the numerator less than the degree of the denominator, while an improper rational expression has a degree of the numerator greater than or equal to the degree of the denominator.

Front

Simplify: (x - 9)/(x + 9)

Back

1/(x - 9)

Front

What is the role of the least common denominator (LCD) in simplifying rational expressions?

Back

The least common denominator is used to combine or compare rational expressions by providing a common base.