describe the error made in subtracting the two rational expressions shown:\n$\frac{1}{x - 2}-\frac{1}{x +…

describe the error made in subtracting the two rational expressions shown:\n$\frac{1}{x - 2}-\frac{1}{x + 1}$\n$=\frac{x + 1}{(x - 2)(x + 1)}-\frac{x - 2}{(x - 2)(x + 1)}$\n$=\frac{-1}{(x - 2)(x + 1)}$

describe the error made in subtracting the two rational expressions shown:\n$\frac{1}{x - 2}-\frac{1}{x + 1}$\n$=\frac{x + 1}{(x - 2)(x + 1)}-\frac{x - 2}{(x - 2)(x + 1)}$\n$=\frac{-1}{(x - 2)(x + 1)}$

Answer

Explanation:

Step1: Identify the common denominator

The common denominator is correctly identified as ((x-2)(x+1)).

Step2: Expand the numerators

Correct expansion should be (1 \cdot (x+1) - 1 \cdot (x-2)), but the solution incorrectly computes the numerator as ((x+1) - (x-2) = x+1 - x + 2 = 3), not (-1).

Step3: Identify the error

The error is in the sign when subtracting the second numerator. The negative sign was not distributed to both terms in ((x-2)), leading to an incorrect numerator calculation.

Answer:

The error is failing to distribute the negative sign to both terms in the second numerator, resulting in an incorrect numerator of (-1) instead of (3).