What is a rational algebraic expression?
A rational algebraic expression is a fraction where both the numerator and denominator are polynomials.
True or False: The expression (x^2 - 1)/(x + 1) is a rational algebraic expression.
True
Fill in the blank: To simplify a rational algebraic expression, you should first factor the __________.
numerator and denominator
What is the first step in simplifying the expression (x^2 - 4)/(x^2 - 2x)?
Factor both the numerator and the denominator.
Which of the following is a common factor of 6x^2 and 9x?
3x
True or False: The expression 1/(x - 2) cannot be simplified further.
True
What does it mean for two expressions to be equivalent?
Two expressions are equivalent if they have the same value for all values of the variable.
Simplify the expression (x^2 - 9)/(x + 3). What is the result?
x - 3
What is the result of simplifying (2x^2 + 4x)/(2x)?
x + 2
Fill in the blank: The expression (x^2 + 5x + 6)/(x + 2) can be simplified by factoring to __________.
x + 3
Which of the following expressions is not a rational algebraic expression?
sqrt(x)/x
True or False: You can cancel terms from the numerator and denominator only if they are factors.
True
What is the simplified form of (x^2 - 4)/(x - 2)?
x + 2
Which operation is typically used to combine like terms in rational expressions?
Addition or subtraction
Fill in the blank: The expression 5/(x^2 - 1) can be simplified using the difference of squares to __________.
5/((x - 1)(x + 1))
What is the domain of the rational expression 1/(x - 3)?
All real numbers except x = 3
True or False: The expression (x^3 - x)/(x^2) can be simplified to x - 1.
False
What is the result of simplifying (x^2 + 2x)/(x^2 + x)?
2/(x + 1)
Fill in the blank: To simplify (x^2 + 4x + 4)/(x + 2), first factor to __________.
(x + 2)(x + 2)/(x + 2)
What is the simplified form of (x^2 - 1)/(x - 1)?
x + 1
Which of the following is a necessary condition for simplifying rational expressions?
Identifying and canceling common factors in the numerator and denominator.
True or False: The expression (3x)/(9x^2) simplifies to 1/3x.
False
What happens to the expression (x^2 - 5x)/(x^2 - 5) when x = 5?
It becomes undefined.
Fill in the blank: The expression (x^2 - 2x)/(x^2 + 2x) can be simplified to __________.
x/(x + 2)
