# Fractions . Simplify [(x^2+3x+2)/(x-2)]*[(x^2-4)/(x-1)].

## Expert Answers

We need to simplify [(x^2+3x+2)/(x-2)]*[(x^2-4)/(x-1)]

[(x^2+3x+2)/(x-2)]*[(x^2-4)/(x-1)]

use x^2 - 4 = (x - 2)(x +2), also let's find the factors of x^2+3x+2

=> [(x^2 + 2x + x +2)/(x-2)]*[(x - 2)(x + 2)/(x-1)]

=> [(x + 2)(x + 1)/(x - 2)]*[(x - 2)(x + 2)/(x-1)]

cancel the common terms in the numerator and denominator

=> (x + 2)^2*(x + 1)/(x - 1)

The simplified form of the given expression is (x + 2)^2*(x + 1)/(x - 1)

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The passage contains a mathematical question asking for the simplification of a given algebraic expression, and it provides a step-by-step solution to the problem.
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Given a text passage, determine:
    1. If it contains a mathematical question (including word problems or calculations)
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First, describe the content structure you found in 1-2 sentences.

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TYPE: <one of the following values>
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- SINGLE_QUESTION
- SINGLE_QUESTION_WITH_ANSWER
- MULTIPLE_QUESTIONS
- MULTIPLE_QUESTIONS_WITH_ANSWERS
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# Fractions . Simplify [(x^2+3x+2)/(x-2)]*[(x^2-4)/(x-1)].

## Expert Answers

We need to simplify [(x^2+3x+2)/(x-2)]*[(x^2-4)/(x-1)]

[(x^2+3x+2)/(x-2)]*[(x^2-4)/(x-1)]

use x^2 - 4 = (x - 2)(x +2), also let's find the factors of x^2+3x+2

=> [(x^2 + 2x + x +2)/(x-2)]*[(x - 2)(x + 2)/(x-1)]

=> [(x + 2)(x + 1)/(x - 2)]*[(x - 2)(x + 2)/(x-1)]

cancel the common terms in the numerator and denominator

=> (x + 2)^2*(x + 1)/(x - 1)

The simplified form of the given expression is (x + 2)^2*(x + 1)/(x - 1)

Approved by eNotes Editorial Team
user
The passage contains a mathematical question asking for the simplification of a given algebraic expression, and it provides a step-by-step solution to the problem.

TYPE: SINGLE_QUESTION_WITH_ANSWER