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In this lesson, we will learn how to divide rational expressions by polynomials or rational expressions involving monomials and/or polynomials.

Q1:

Answer the following questions for the rational expressions 5 π₯ β 4 5 π₯ 1 2 π₯ β 4 π₯ 3 2 and 1 5 π₯ β 4 5 3 π₯ 2 .

Evaluate 5 π₯ β 4 5 π₯ 1 2 π₯ β 4 π₯ 3 2 divided by 1 5 π₯ β 4 5 3 π₯ 2 .

Is the result of 5 π₯ β 4 5 π₯ 1 2 π₯ β 4 π₯ 3 2 divided by 1 5 π₯ β 4 5 3 π₯ 2 a rational expression?

Would this be true for any rational expression divided by another rational expression?

Q2:

Simplify the function π ( π₯ ) = π₯ + 5 π₯ + 9 π₯ + 2 0 Γ π₯ + 1 5 π₯ + 5 4 7 π₯ + 6 9 π₯ + 5 4 2 2 2 , and determine its domain.

Q3:

Simplify 1 4 π₯ β 2 1 π₯ 4 π₯ β 2 0 Γ· 4 π₯ β 6 2 π₯ β 1 2 .

Q4:

Find the volume of a cube whose side length is 4 5 π₯ .

Q5:

Determine the domain of the function π ( π₯ ) = π₯ β π₯ β 6 π₯ β 4 Γ· 2 π₯ β 6 π₯ β 4 π₯ + 4 2 2 2 .

Q6:

Determine the domain of the function π ( π₯ ) = 3 π₯ β 1 5 π₯ β 6 Γ· 6 π₯ β 3 0 4 π₯ β 2 4 .

Q7:

Given the function π ( π₯ ) = π₯ β 6 π₯ β 1 5 π₯ + 5 4 Γ π₯ β 3 π₯ β 2 8 2 π₯ β 1 5 π₯ + 7 2 2 2 , evaluate π ( 7 ) , if possible.

Q8:

Simplify the function π ( π₯ ) = π₯ + 3 4 3 2 π₯ + 1 4 π₯ Γ π₯ + 3 π₯ β 7 π₯ + 4 9 3 2 2 , and determine its domain.

Q9:

Simplify the function π ( π₯ ) = π₯ + 1 6 π₯ + 6 4 π₯ + 8 π₯ Γ 7 π₯ β 5 6 6 4 β π₯ 2 2 2 , and determine its domain.

Q10:

Simplify 4 π₯ β 3 π₯ 2 π₯ β 1 β 2 π₯ β 5 4 π₯ β 2 2 .

Q11:

Simplify the function π ( π₯ ) = π₯ β 1 2 π₯ + 3 6 π₯ β 2 1 6 Γ· 7 π₯ β 4 2 π₯ + 6 π₯ + 3 6 2 3 2 , and determine its domain.

Q12:

Simplify the function π ( π₯ ) = π₯ β 1 6 2 π₯ + 9 π₯ Γ· 9 π₯ β 7 2 π₯ + 1 4 4 4 π₯ β 8 1 2 2 2 2 .

Q13:

Simplify 6 π₯ β 3 π₯ 3 π₯ β 2 Γ 7 π₯ β 1 4 2 π₯ β 1 3 2 .

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