4-3 Simplify Rational Expressions

Front

What is a rational expression?

Back

A rational expression is a fraction where the numerator and the denominator are both 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 for a rational expression to be undefined?

Back

A rational expression is undefined when its denominator equals zero.

Front

What are the domain restrictions for the expression (x-4)/(x+3)?

Back

x ≠ -3 (the denominator cannot be zero).

Front

How do you find the values that make a rational expression undefined?

Back

Set the denominator equal to zero and solve for x.

Front

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

Back

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

Front

What is the domain of the expression (x^2 - 1)/(x^2 - 4)?

Back

x ≠ 2 and x ≠ -2 (the values that make the denominator zero).

Front

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

Back

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

Front

If f(x) = (x^2 - 1)/(x - 1), what is f(1)?

Back

f(1) is undefined because the denominator becomes zero.

Front

What is the first step in simplifying the expression (x^2 - 5x + 6)/(x - 2)?

Back

Factor the numerator to (x - 2)(x - 3) and then cancel the common factor.