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 by canceling common factors in the numerator and denominator.

Front

What is the first step in simplifying the expression (8x + 32)/(x + 4)?

Back

Factor the numerator: 8(x + 4)/(x + 4).

Front

What happens to the expression (8x + 32)/(x + 4) after canceling common factors?

Back

It simplifies to 8.

Front

How do you find excluded values in a rational expression?

Back

Excluded values are found by setting the denominator equal to zero and solving for the variable.

Front

What is the excluded value for the expression 7/(x - 3)?

Back

The excluded value is 3.

Front

What does it mean if a rational expression is undefined?

Back

A rational expression is undefined when its denominator equals zero.

Front

How do you simplify the expression (x^2 + 6x + 8)/(x^2 - x - 6)?

Back

Factor both the numerator and denominator: (x + 2)(x + 4)/((x - 3)(x + 2)), then cancel (x + 2) to get (x + 4)/(x - 3).

Front

What is the simplified form of (x + 6)/(x - 5)?

Back

The expression is already in its simplest form.

Front

What is the significance of the expression (x^2 + 6x + 8)/(x^2 - x - 6) in rational expressions?

Back

It demonstrates how to factor and simplify complex rational expressions.