Question

What mistake did Lindsay make?

Answer 1

Answer:

Step-by-step explanation:

Discussion and Correction

The algrebra  itself is fine. The exclusions are not so good. The difficulty comes in the denominator. It factors into (2x)(x - 3). x cannot take on a value of 0 (that was pointed out and that is correct). The problem comes in the plus/minus 3. Plus 3 is correct. x - 3 will come 0 if x = 3. Nothing bad will happen if x = - 3

Answer: So the exclusions in the denominator should be modified to x = 3.

Answer 2

Answer:

The excluded values are x-values that make the denominator of the original expression zero, since $\dfrac{a}{0}$ is undefined.

$x = -3$ is not an excluded value since this x-value does not make the  denominator zero.

$x = -3$ makes the numerator zero, but as $\dfrac{0}{a}=0$ it is not an excluded value.

Therefore, step 3 of her work should read:

$\textsf{Finding excluded values}:x\neq 0\:\textsf{and}\:x\neq 3$