Rational Expression Restrictions

Front

What is a rational expression?

Back

A rational expression is a fraction where the numerator and the denominator are both polynomials.

Front

What is the restriction on the rational expression \( \frac{x^2-9}{x-3} \)?

Back

x cannot be equal to 3.

Front

How do you find the excluded values of a rational expression?

Back

Set the denominator equal to zero and solve for the variable.

Front

What are excluded values in the context of rational expressions?

Back

Excluded values are the values of the variable that make the denominator zero, resulting in an undefined expression.

Front

If a rational expression has a denominator of \( x^2 - 4 \), what are the excluded values?

Back

x = 2 and x = -2.

Front

What is the significance of identifying restrictions in rational expressions?

Back

Identifying restrictions is crucial to avoid division by zero, which makes the expression undefined.

Front

What happens to a rational expression if you multiply the numerator and denominator by the same non-zero value?

Back

The value of the rational expression remains unchanged.

Front

What is the domain of a rational expression?

Back

The domain is the set of all real numbers except for the excluded values.

Front

How can you simplify a rational expression?

Back

Factor both the numerator and denominator and cancel out any common factors.

Front

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

Back

A rational expression is a fraction of polynomials, while a rational number is a fraction of integers.