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

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 reduce a fraction?

Back

To reduce a fraction means to simplify it to its lowest terms by dividing both the numerator and the denominator by their greatest common factor.

Front

What is the greatest common factor (GCF)?

Back

The greatest common factor is the largest factor that two or more numbers share.

Front

Simplify: (x^2 - 9)/(x + 3)

Back

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

Front

What is the difference between a polynomial and a rational expression?

Back

A polynomial is an expression made up of variables and coefficients, while a rational expression is a ratio of two polynomials.

Front

What is the first step in simplifying (2x^2 + 4x)/(2x)?

Back

Factor out the common factor in the numerator: 2x(x + 2)/(2x), then cancel the common factor 2x.

Front

Simplify: (x^2 - 4)/(x - 2)

Back

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

Front

What is a polynomial?

Back

A polynomial is an algebraic expression that consists of variables raised to whole number powers and coefficients.

Front

What does it mean to factor an expression?

Back

Factoring an expression means rewriting it as a product of its factors.