Question
Marie divided the expression x2−4x−216x2÷x2−9x2−3x
incorrectly.
First, Marie took the reciprocal of the second term and multiplied: x2−4x−216x2⋅x2−3xx2−9
.
Next, Marie factored each of the terms: (x−7)(x+3)6x2⋅x(x−3)(x+3)(x−3)
.
Finally, Marie canceled terms that were in common and got the answer: x(x−7)6x2
.
Which of the following options explains Marie’s error?
Option #1: Marie factored incorrectly.
Option #2: Marie canceled incorrectly.
Option #3: Marie did not fully simplify the expression.
(1 point)
Option #
shows Marie’s error.
The answer to this question is Option #2: Marie canceled incorrectly.
In the given expression, Marie mistakenly canceled out the common factors (x+3) and (x-3) without multiplying them back with the remaining terms. This caused her to lose those factors in her final answer. Thus, Marie's error lies in her cancellation step.
Option #2: Marie canceled incorrectly.
The error in Marie's calculation can be explained by Option #2: Marie canceled incorrectly.
Marie made a mistake by canceling out the common term (x+3) from both the numerator and denominator of the expression. Canceling terms should only be done when they are factors of both the numerator and the denominator, which is not the case here.
In this example, the factor (x+3) appears in both the numerator and the denominator, but it cannot be canceled out because it is being multiplied by other terms. Canceling out (x+3) would result in an incorrect simplification of the expression.
Therefore, the correct explanation for Marie's error is that she canceled incorrectly, as mentioned in Option #2.