Simplifying Rational Expressions with Common Monomial Factors

What values of x make the initial rational expression undefined?

• x = -1

• x = 1

• x = 2

• x = 0

What common factors are found in both the numerator and the denominator?

• x and 2

• 7 and 14

• x and 14

• x and 7

After factoring, what expression is left in the numerator?

• 2x + 1

• x + 2

• 2x - 1

• x - 2

Why is it important to maintain the constraint x ≠ 0 in the simplified expression?

• To define a new function

• To keep the expressions algebraically equivalent

• To make the expression undefined at x = 0

• To simplify the expression further

What is the simplified form of the expression after canceling out common factors?

• (x - 1) / 2

• (x + 1) / 2

• (2x + 1) / 2

• (2x - 1) / 2

What additional value of z makes the new complex expression undefined?

• z = 2

• z = 1/2

• z = 3

• z = 3/2

What common factors are factored out from the new complex expression?

• z squared

• 34z squared

• 17z

• 17z squared

What is the simplified form of the complex expression after factoring?

• (z - 1) / (2z - 3)

• (z + 1) / (2z + 3)

• (z - 1) / (2z + 3)

• (z + 1) / (2z - 3)

Why is the constraint z ≠ 0 still necessary in the simplified complex expression?

• Because z = 0 simplifies the expression further

• To maintain algebraic equivalence with the original

• To make the expression undefined at z = 0

• To avoid division by zero in the original expression

What does the term 'algebraically equivalent' imply about the simplified expressions?

• They are simpler than the original

• They have the same domain restrictions as the original

• They have different domain restrictions

• They are completely new expressions