Operations with 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 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 (x^2 - 9)/(x + 3)?

Back

The first step is to factor the numerator as (x - 3)(x + 3) and then cancel the common factor (x + 3).

Front

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

Back

The result is (x/2) after canceling the common factor of 2x.

Front

What is the significance of identifying restrictions in rational expressions?

Back

Identifying restrictions is important because it determines the values of the variable that make the denominator zero, which are not allowed.

Front

What are the restrictions for the expression (x + 1)/(x - 2)?

Back

The restriction is x ≠ 2, as this value would make the denominator zero.

Front

How do you add two rational expressions with different denominators?

Back

To add two rational expressions with different denominators, find a common denominator, rewrite each expression, and then combine the numerators.

Front

What is the process for subtracting rational expressions?

Back

The process is similar to addition: find a common denominator, rewrite the expressions, and then subtract the numerators.

Front

What is the result of multiplying (x + 2)/(x - 1) by (x - 1)/(x + 3)?

Back

The result is (x + 2)/(x + 3) after canceling the common factor (x - 1).