Simplifying Rational Algebraic Expressions

Front

What is a rational algebraic expression?

Back

A rational algebraic 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 by canceling common factors in the numerator and denominator.

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 factor the expression x^2 - 4?

Back

x^2 - 4 can be factored as (x - 2)(x + 2) using the difference of squares.

Front

What is the result of simplifying 4x^3/(2x)?

Back

The result is 2x^2.

Front

What is the importance of identifying restrictions in rational expressions?

Back

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

Front

How do you find the restrictions for the expression 1/(x - 3)?

Back

The restriction is x ≠ 3, as this value would make the denominator zero.

Front

What is the simplified form of (x^2 - 1)/(x - 1)?

Back

The simplified form is x + 1, after factoring the numerator as (x - 1)(x + 1) and canceling the common factor.

Front

What does it mean to have a common factor in rational expressions?

Back

A common factor is a term that appears in both the numerator and the denominator, which can be canceled out during simplification.

Front

How do you simplify the expression (3x^2)/(6x)?

Back

The simplified form is 1/2x.