Error Analysis Math Example 4

Follow the full solution, then compare it with the other examples linked below.

Example 4

medium

A student cancels incorrectly:

\dfrac{x^2+3x}{x} = x^2+3

. Identify and correct the error.

Solution

1
Error: the student cancelled $x$ from $x^2$ but left the $3x$ incorrectly. $\frac{x^2+3x}{x} = \frac{x \cdot x + 3 \cdot x}{x} = \frac{x(x+3)}{x} = x+3$ .
2
The student's answer $x^2+3$ is dimensionally wrong — $\frac{x^2}{x} = x$ , not $x^2$ .
3
Correct answer: $x+3$ (for $x \ne 0$ ).

Answer

\frac{x^2+3x}{x} = x+3 \quad (x \ne 0)

Cancellation in fractions applies to common factors of the entire numerator and denominator, not individual terms. Factor first, then cancel. The error here was cancelling

x

from only one term of the numerator.

About Error Analysis

The systematic study of how errors arise in calculations or models, how large they are, and how they propagate through subsequent steps.

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More Error Analysis Examples

Example 1 easy

A student writes: '[formula].' Identify the error and find a numerical counterexample.

Example 2 medium

A student 'proves': '[formula] for all [formula]' by checking [formula]. Identify the error in this

Example 3 easy

Find the error: a student solves [formula] by writing [formula], then [formula]. What went wrong?

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