Simplifying Rational Expressions: Key Concepts and Techniques

What is a rational expression?

• A polynomial subtracted from another polynomial

• A polynomial added to another polynomial

• A polynomial multiplied by another polynomial

• A polynomial divided by another polynomial

What is a common mistake when simplifying rational expressions?

• Incorrectly canceling terms that are being added or subtracted

• Factoring out the greatest common factor

• Correctly applying the distributive property

• Using the quadratic formula

How should one correctly simplify a rational expression?

• By factoring out common factors and then canceling

• By canceling out terms individually

• By adding a constant to both the numerator and denominator

• By multiplying the numerator and denominator by the same number

What does it mean to factor out a common factor in a rational expression?

• To subtract a common factor from both the numerator and the denominator

• To add a common factor to both the numerator and the denominator

• To multiply both the numerator and the denominator by their lowest common multiple

• To divide both the numerator and the denominator by their highest common factor

In the expression 2x + 2 divided by 2, what is the correct simplification?

• 1

• x

• 2x

• x + 1

Why is it incorrect to cancel terms that are being added or subtracted directly?

• Because it violates the fundamental theorem of algebra

• Because it simplifies the expression too much

• Because it changes the value of the expression

• Because it is only permissible in trigonometry

What is the correct simplification process for a rational expression?

• Multiply numerator and denominator by the highest common factor

• Factor out common factors, then cancel

• Cancel out terms directly without factoring

• Add the same number to both numerator and denominator

What is the result of simplifying the expression 20x + 10 all divided by 30x + 15?

• 2/3

• 2x + 1

• 10x + 5

• x/2

What must be considered when simplifying expressions to avoid errors?

• The type of polynomial

• The coefficients of the terms

• The degree of the polynomial

• The domain of the expression

What happens to the expression 20x + 10 all divided by 30x + 15 when x equals -1/2?

• It simplifies to 0

• It equals 2/3

• It remains unchanged

• It becomes undefined