AnswersPARTA - EVP PGCPS ALGEBRA 2 OC FALL2026 - 793033Multiplying and Dividing Rational Expressions

Multiplying and Dividing Rational Expressions Answers

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Find the simplified product.

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Simplify the product

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Mathias found the product [image 1] as follows. [image 2] Which of the following best describes his error?

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He did not multiply the denominators correctly.
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He did not factor the first numerator.
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He did not divide out the 2 from the 4 and the 8.
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He did not distribute the 5 to the terms in the other numerator.
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Which multiplication expression is equivalent to ?

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Find the simplified quotient.

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t – 6
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3t + 18
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3t – 18
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Simplify .

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x2 + 3x
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Simplify.X 4m7m12m36m

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X 4m
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36m
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Using V = lwh , find an expression in factored form for the volume of this prism. Explain the general steps you used to arrive at this answer.

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Answer:

To find the volume of the rectangular prism, use the formula V = lwh. 1. Substitute the given expressions into the formula: V = [(24x^2 + 6x) / (x - 1)] * (2x - 5) * [(x^2 - x) / (4x + 1)]. 2. Write 2x - 5 as a fraction over 1: (2x - 5) / 1. 3. Factor the expressions where possible: - 24x^2 + 6x factors to 6x(4x + 1). - x^2 - x factors to x(x - 1). 4. Rewrite the volume expression with factored components: V = [6x(4x + 1) / (x - 1)] * [(2x - 5) / 1] * [x(x - 1) / (4x + 1)]. 5. Divide out (cancel) the common factors found in the numerator and denominator, which are (4x + 1) and (x - 1). 6. Multiply the remaining factors: V = (6x) * (2x - 5) * (x), which simplifies to (x)(6x)(2x - 5) or 6x^2(2x - 5).

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Select all of the following that you included in your answer.

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Write 2x – 5 over 1.
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Factor numerators and denominators, when possible
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Divide out common factors to simplify.
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Determine that the volume is (x)(6x)(2x – 5).
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The simplified quotient is .

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