Question

What mistake did Lindsay make?

Answer 1

The excluded values are x-values that make the denominator of the original expression zero, since
`(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
`(0)/(a)=0` it is not an excluded value.

Therefore, step 3 of her work should read:

`\textsf{Finding excluded values}:x\\eq 0\:\textsf{and}\:x\\eq 3`

Answer 2

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.