What error was made in subtracting the two rational expressions?…

Mathematics Questions

Describe the error made in subtracting the two rational expressions shown:

Short Answer

The first step in fraction subtraction is to establish a common denominator, allowing for accurate combination and simplification. Next, rewrite the fractions according to this denominator, and finally perform the subtraction of the numerators, resulting in 3.

Step-by-Step Solution

Step 1: Establish the Common Denominator

The first crucial step in the calculation is to identify and establish the common denominator for the fractions involved. This ensures that the fractions can be accurately combined and simplified. After finding the common denominator, adjust each fraction accordingly so they can be expressed uniformly.

Step 2: Rewrite the Expressions

Once the common denominator is set, the next step is to rewrite each fraction to reflect this denominator. It is essential to change the expressions correctly, allowing for accurate subtraction later on. This means carefully adjusting both the numerators and denominators while keeping their values equivalent.

Step 3: Perform the Subtraction

Finally, proceed with the subtraction of the numerators, where the expression should be calculated as follows: (x+1) – (x-2). It is important to distribute the subtraction properly; this translates to x + 1 – x + 2. As a result, the x terms will cancel each other out, leading to a final result of 1 + 2 = 3.

Related Concepts

Common Denominator

The shared multiple of the denominators of two or more fractions that allows them to be combined or compared

Rewrite

The process of adjusting fractions to have the same denominator while maintaining their equivalent values

Subtraction

The mathematical operation of removing one quantity from another, specifically applied to the numerators of fractions once a common denominator is established.

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