In Exercises 83–90, perform the indicated operations. Simplify the result, if possible. (2−6/(x+1))(1 + 3/(x−2))

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Distribute the terms in the expression (2 - 6/(x+1))(1 + 3/(x-2)) using the distributive property: multiply each term in the first parenthesis by each term in the second parenthesis.

The first multiplication is 2 * 1, which simplifies to 2.

The second multiplication is 2 * (3/(x-2)), which simplifies to 6/(x-2).

The third multiplication is (-6/(x+1)) * 1, which simplifies to -6/(x+1).

The fourth multiplication is (-6/(x+1)) * (3/(x-2)), which simplifies to -18/((x+1)(x-2)). Combine all these terms into a single expression and simplify further if possible.

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Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

Algebraic Expressions

Algebraic expressions are mathematical phrases that can include numbers, variables, and operators. Understanding how to manipulate these expressions is crucial for performing operations such as addition, subtraction, multiplication, and division. In the given question, the expressions involve fractions and require simplification, which is a common task in algebra.

Multiplication of Fractions

Multiplying fractions involves multiplying the numerators together and the denominators together. This concept is essential for simplifying expressions that contain fractions, as seen in the problem. Recognizing how to handle fractions correctly ensures accurate results when performing operations on algebraic expressions.

Simplification of Expressions

Simplification is the process of reducing an expression to its simplest form. This involves combining like terms, reducing fractions, and eliminating unnecessary parentheses. In the context of the question, simplifying the result after performing the indicated operations is key to presenting a clear and concise answer.