Simplifying and Multiplying Rational Expressions

This lesson covers rational expressions, including their definition, simplification, and operations like multiplication and division. It also explores domain restrictions and provides examples to illustrate these concepts. Additionally, the lesson compares the volume to surface area ratios of a cube and a sphere to determine packaging efficiency. The session concludes with practice problems to reinforce the learning objectives.

What is a rational expression?

• A difference of two polynomials

• A product of two polynomials

• A sum of two polynomials

• A quotient of two polynomials

When is a rational expression in its simplest form?

• When the denominator is zero

• When the numerator is zero

• When the numerator and denominator have no common factors other than 1

• When the numerator and denominator are equal

How do you determine where a rational expression is undefined?

• When the expression is negative

• When the denominator is zero

• When the numerator is zero

• When both numerator and denominator are zero

What are the domain restrictions for the expression (x+4)/(x-3)?

• x ≠ 4

• x ≠ -3

• x ≠ 0

• x ≠ 3

What is the first step in multiplying two rational expressions?

• Subtract the denominators

• Add the numerators

• Multiply the numerators and denominators separately

• Divide the numerators

What should you do when dividing two rational expressions?

• Divide the numerators and denominators separately

• Subtract the second expression from the first

• Add the two expressions

• Multiply by the reciprocal of the second expression

If the height of a cube is equal to the diameter of a sphere, what is the relationship between the side length of the cube (s) and the radius of the sphere (r)?

• s = 4r

• s = r

• s = r/2

• s = 2r

What is the volume to surface area ratio for a cube with side length s?

• s/4

• s/2

• s/3

• s/6

In the expression 8x^2y / (x+1) * (x+1) / 6xy^2, what can be eliminated?

• 6

• x+1

• y

• x

What are the restrictions for the expression (x+1)(x-1)/(x+3)(x-3) * (x+5)(x+3)/(x+4)(x-1)?

• x ≠ -3, 3, -4, 1, -5

• x ≠ 3, -3, 4, -1, 5

• x ≠ -3, 3, 4, -1, 5

• x ≠ 3, -3, -4, 1, 5