6.3 rational

What are non-permissible values in rational expressions?

Values that make the denominator zero.

How do you simplify a rational expression?

Factor the numerator and denominator, then cancel common factors.

What happens when you add rational expressions with different denominators?

Find a common denominator before combining the numerators.

What is the first step in subtracting rational expressions?

Ensure both expressions have a common denominator.

How do you identify non-permissible values in an expression like (x-3)(x+1)?

Set each factor equal to zero and solve for x.

What is the result of adding 1/(x-2) and 1/(x+3)?

Combine over the common denominator (x-2)(x+3).

What distinguishes adding from subtracting rational expressions?

Subtraction requires changing the sign of the second numerator.

What is the implication of simplifying 3x + 15 over 4x²?

It reduces to (3(x + 5))/(4x²) for easier manipulation.

What do you do if a rational expression has a common factor in the numerator and denominator?

Cancel the common factor to simplify the expression.

What is the consequence of having a denominator of x² - 4?

x cannot equal 2 or -2, as these make the denominator zero.