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Answer :
Final answer:
Morgan likely forgot to distribute the negative sign to two terms in a subtraction involving rational expressions, which is a common error. Properly distributing the negative sign to each term in the expression is critical for accurate calculations.
Explanation:
Morgan's error in subtracting the rational expressions was most likely that she forgot to distribute the negative sign to two of the terms in the second expression. This is a common mistake when dealing with rational expressions and can lead to incorrect results. The correct process involves ensuring that the negative sign (or subtraction) is applied to each term within the parentheses.
For example, if we have an expression like 5 - (3 + 2), we must subtract each term inside the parentheses from 5 which will be 5 - 3 - 2, resulting in 0. But if we mistakenly distribute the negative sign only to the first term, we would erroneously calculate it as 5 - 3 + 2 which incorrectly yields 4.
Furthermore, addition and subtraction of rational expressions require combining only like terms and maintaining the common denominator without alteration. Keep in mind that common denominators are crucial in the process, and we should never add or subtract the denominators but only the numerators when they are like terms.
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