Simplifying Rational Expressions in Algebra II

The video tutorial introduces the concept of simplifying fractions by finding common factors and reducing them to their lowest terms. It then extends these principles to rational expressions, which involve variables in the numerator and denominator. The tutorial emphasizes the importance of excluding values that make the denominator zero, rendering the expression undefined. Advanced factoring techniques are demonstrated, highlighting common mistakes and the need for careful calculation.

What is the lowest term of the fraction 8/24?

• 1/2

• 3/4

• 2/3

• 1/3

What is the common factor in the rational expression 9x + 3 over 12x + 4?

• 3

• 4

• 3x + 1

• x + 4

When simplifying the rational expression x^2 - 9 over 5x + 15, what value must be excluded for x?

• 0

• 3

• -3

• 5

In the expression x^2 + 6x + 5 over x^2 - x - 2, what are the factors of the numerator?

• (x + 3)(x - 2)

• (x + 2)(x - 3)

• (x + 1)(x - 5)

• (x + 5)(x - 1)

What condition must be added to the simplified form of x^2 + 6x + 5 over x^2 - x - 2 to make it valid?

• x cannot be 1

• x cannot be 2

• x cannot be -1

• x cannot be 0

What is the first step in factoring the expression 3x^2 + 3x - 18?

• Group terms

• Split the middle term

• Factor out a 3

• Find common factors

What are the two numbers that multiply to -54 and add to 3 in the expression 3x^2 + 3x - 18?

• 9 and -6

• 6 and -9

• 18 and -3

• 3 and -18

What is the factored form of the denominator 2x^2 + 5x - 3?

• (2x - 1)(x + 3)

• (2x + 1)(x - 3)

• (2x - 3)(x + 1)

• (2x + 3)(x - 1)

What condition must be added to the simplified form of 3x^2 + 3x - 18 over 2x^2 + 5x - 3?

• x cannot be 1

• x cannot be 3

• x cannot be -3

• x cannot be -1

What is the simplified form of the rational expression 3x^2 + 3x - 18 over 2x^2 + 5x - 3?

• (3x - 6)/(2x + 1)

• (3x + 6)/(2x - 1)

• (3x + 6)/(2x + 1)

• (3x - 6)/(2x - 1)