Simplifying Rational Expressions: Key Concepts and Techniques

What is a rational number?

• A number that can be expressed as a fraction a/b where a and b are integers and b is not zero.

• A number where the denominator must be zero.

• Any integer value.

• A number that cannot be expressed as a fraction.

What must you always remember when simplifying fractions?

• Convert them into decimals.

• Only simplify the numerator.

• Reduce them to their lowest terms.

• Ignore any variables.

What does factoring help to identify in rational expressions?

• Complex number components

• Common factors in the numerator and denominator

• Decimal expansions

• Numerical coefficients only

What is a restriction in the context of rational expressions?

• A method to simplify the expression further.

• A value that makes the denominator zero, thus undefined.

• A value that makes the expression equal to one.

• A rule that allows any value for variables.

In the given example, what is the simplest form of the expression if the numerator is 2x+4 and the denominator is 3(x+2)?

• 3x with x not equal to 2

• 2/3 with x not equal to -2

• x+2 with x not equal to -2

• 2/3 with no restrictions

What happens to the expression if x equals one of the restricted values?

• The expression simplifies to zero.

• The expression becomes undefined.

• The expression simplifies to one.

• The expression does not change.

Why is it important to check for restrictions in rational expressions?

• To identify potential maximum and minimum values.

• To convert the expression into a polynomial.

• To simplify the expression to its lowest terms.

• To ensure the expression is always defined.

Why does the expression 2x-9 and 9-2x only cancel to leave a negative?

• Because they are identical.

• Because subtraction order does not matter.

• Because they are not identical but opposites, hence the negative.

• Because they do not have any common factors.

What is the result of simplifying the expression with a numerator of x^3 - 8 and a denominator of x-2?

• x^2 - 2x - 4 with x not equal to 2

• x^2 + 2x + 4 with x not equal to 2

• x^2 - 2x + 4 with x not equal to 2

• x^2 + 2x - 4 with x not equal to 2

What are the restrictions for the expression where the denominator factors are x+4 and x-1?

• x cannot equal -4 or -1

• x cannot equal 4 or -1

• x cannot equal -4 or 1

• x cannot equal 4 or 1