Simplifying Rational Expressions in Algebra

This lesson covers simplifying rational expressions by identifying and canceling common factors. It explains how to determine when expressions are undefined due to variables in the denominator. The video provides step-by-step solutions to example problems, demonstrating the simplification of complex rational expressions.

What is the first step in simplifying a rational expression?

• Multiply the numerator by the denominator

• Divide the numerator by the denominator

• Cancel out any common terms immediately

• Identify the numerator and denominator

What must be true for a term to be cancelled in a rational expression?

• The term must be a number

• The term must be an exponent

• The term must be a common factor in every term of both numerator and denominator

• The term must appear in the numerator only

What should you always state when dealing with variables in the denominator?

• The minimum value of the expression

• The possible values of the numerator

• The values for which the expression is undefined

• The maximum value of the denominator

How can you determine the values for which a rational expression is undefined?

• Add one to the denominator

• Subtract the numerator from the denominator

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

• Multiply the denominator by zero

What is the greatest common factor method used for in rational expressions?

• To simplify by factoring out common terms

• To subtract fractions

• To multiply fractions

• To add fractions

What happens if a rational expression cannot be simplified further?

• It remains in its original form

• It automatically simplifies to 1

• It is considered undefined

• It must be discarded

In simplifying the expression 3x(x - 1) over 9x^2 - 15x, what common factor is cancelled?

• 3x

• 9x

• x - 1

• 15x

What is the simplified form of the expression 4x + 28 over 3x^2 + 21x?

• 4 over 3x

• 4x over 3x

• 28 over 21x

• x + 7 over x

What value of x makes the expression 3x + 5 = 0 undefined?

• x = 0

• x = 3/5

• x = -5/3

• x = 5/3

Which of the following is a correct statement about simplifying rational expressions?

• You can always cancel x terms regardless of their placement

• Only coefficients can be cancelled, not variables

• Common factors in both numerator and denominator can be cancelled

• Expressions are undefined if they contain any variables