Simplifying Complex Rational Expressions

This video tutorial reviews complex rational expressions, which are algebraic fractions with fractions in their numerators or denominators. It explains two methods for simplifying these expressions: simplifying the numerator and denominator separately, and using the least common denominator (LCD) for a more efficient process. The tutorial provides detailed examples to illustrate both methods, emphasizing the efficiency of the LCD approach.

What is a complex rational expression?

• A fraction with variables only.

• A fraction with only numbers.

• A fraction with another fraction in the numerator or denominator.

• A fraction with a polynomial in the numerator and denominator.

What is the first step in the slower method of simplifying complex rational expressions?

• Subtract the fractions.

• Add the fractions together.

• Simplify the numerator and denominator separately.

• Multiply the numerator and denominator by the LCD.

In the faster method, what do you multiply the numerator and denominator by?

• The least common multiple.

• The highest power of the variable.

• The least common denominator.

• The greatest common factor.

What is the LCD of the fractions 1/3 and 3/(x-2)?

• 1

• 3(x-2)

• x-2

• 3

What happens when you multiply a fraction by its reciprocal?

• The fraction halves.

• The fraction doubles.

• The fraction becomes one.

• The fraction becomes zero.

What is the result of factoring x^2 - 8x + 33?

• (x-3)(x-11)

• (x-5)(x-6)

• (x-1)(x-33)

• Prime polynomial