Simplifying Algebraic Fractions

What is the significance of the zero product property in algebra?

• It states that the sum of two factors is zero.

• It states that if the product of two factors is zero, at least one of the factors must be zero.

• It indicates that the product of any number and zero is always one.

• It shows that factors can be negative or positive.

What is the first step in simplifying @@\frac{x^2+6x+9}{x^2-9}@@?

• Factor the numerator and the denominator: @@\frac{(x+3)(x+3)}{(x+3)(x-3)}@@

• Combine like terms in the numerator and denominator.

• Multiply both the numerator and denominator by the same expression.

• Add the numerator and denominator together.

How do you simplify an algebraic fraction?

• By adding the numerator and denominator together.

• By multiplying the numerator and denominator by the same number.

• To simplify an algebraic fraction, factor both the numerator and the denominator and then cancel any common factors.

• By dividing the numerator by the denominator.

What is the simplified form of @@\frac{x^2+6x+9}{x^2-9}@@?

• @@\frac{x+3}{x-3}@@

• @@\frac{x+3}{x+3}@@

• @@\frac{x-3}{x+3}@@

• @@\frac{x^2+3}{x^2-3}@@

What is the simplified form of @@\frac{x^2-5x+6}{x^2-4} \cdot \frac{x^2-3x+2}{x^2-9}@@?

• @@\frac{(x-2)(x-1)}{(x+2)(x+3)}@@

• @@\frac{(x-3)(x-2)}{(x+1)(x+4)}@@

• @@\frac{(x-1)(x-6)}{(x-2)(x+2)}@@

• @@\frac{(x-2)(x-3)}{(x+1)(x+3)}@@

What is the difference between a proper and improper fraction?

• A proper fraction has a numerator larger than the denominator, while an improper fraction has a numerator smaller than the denominator.

• A proper fraction has a numerator smaller than the denominator, while an improper fraction has a numerator larger than or equal to the denominator.

• A proper fraction has a numerator equal to the denominator, while an improper fraction has a numerator smaller than the denominator.

• A proper fraction has a numerator larger than or equal to the denominator, while an improper fraction has a numerator smaller than the denominator.

What is the simplified form of @@\frac{x^2+6x+9}{x^2-2x-15}@@?

• @@\frac{x+3}{x-5}@@

• @@\frac{x+5}{x-3}@@

• @@\frac{x-3}{x+5}@@

• @@\frac{x+2}{x-4}@@

What is the definition of a rational expression?

• A rational expression is a fraction where both the numerator and the denominator are polynomials.

• A rational expression is a type of irrational number.

• A rational expression is a polynomial with a variable in the denominator.

• A rational expression is a fraction that cannot be simplified.

What is a common factor in algebraic fractions?

• A factor that appears only in the numerator.

• A factor that appears only in the denominator.

• A factor that appears in both the numerator and the denominator, which can be canceled out.

• A factor that is unique to the fraction and cannot be simplified.

How do you identify the domain of a rational expression?

• The domain is all real numbers except where the denominator equals zero.

• The domain is all integers only.

• The domain includes only positive numbers.

• The domain is all real numbers including where the denominator equals zero.