Simplifying Rational Expressions

This video tutorial introduces rational expressions, explaining their definition and domain. It covers the process of simplifying these expressions by factoring and removing common factors. The tutorial provides several examples, ranging from basic to advanced, demonstrating how to simplify rational expressions while considering domain restrictions. The video concludes with a summary of key points and additional examples to reinforce learning.

What is a rational expression?

• A fraction where both numerator and denominator are integers.

• A fraction where both numerator and denominator are polynomials.

• A fraction where the numerator is a polynomial and the denominator is an integer.

• A fraction where the numerator is an integer and the denominator is a polynomial.

What must be true about the denominator of a rational expression?

• It can be any real number.

• It must be a positive integer.

• It must be a polynomial of degree one.

• It cannot be zero.

What is the first step in simplifying a rational expression?

• Factor the numerator and denominator completely.

• Multiply the numerator and denominator by a common factor.

• Add the numerator and denominator.

• Divide the numerator by the denominator.

When simplifying a rational expression, what can be canceled?

• Only the coefficients of the terms.

• Common factors in the numerator and denominator.

• Only the variables in the terms.

• Any terms in the numerator and denominator.

In the example with 10x^3y^2/25x^2y^2, what is the simplified form?

• x^3y^2/x^2y^2

• 10x/25

• 5x/2

• 2x/5

Why can't you simplify across addition in a rational expression?

• Because addition is only allowed in the numerator.

• Because addition is not allowed in rational expressions.

• Because terms connected by addition are not common factors.

• Because addition changes the value of the expression.

What is the result of simplifying (x^2 - 9)/(x^2 - 5x + 6)?

• (x + 3)/(x - 2)

• (x - 3)/(x - 2)

• (x - 3)/(x - 5)

• (x + 3)/(x - 3)

In the expression 3x^2 - 10x - 8, what are the factors?

• (3x - 2)(x + 4)

• (3x + 2)(x - 4)

• (3x - 4)(x + 2)

• (3x + 4)(x - 2)

What is the simplified form of (x - 7)/(3(7 - x))?

• -1/3

• 1/3

• 3

• -3

Why is it important to consider the original expression when simplifying?

• To ensure the simplified expression is more complex.

• To ensure the simplified expression is defined for the same values.

• To ensure the simplified expression has more terms.

• To ensure the simplified expression is easier to understand.