Question

1.) Simplify. x/6x-x^2

A. 1/6-x; where x ≠ 0, 6
B. 1/6-x; where x ≠ 6* (My answer)
C. 1/6x; where x ≠ 0
D. 1/6

2.) Simplify. -12x^4/x^4+8x^5

A. -12/1+8x; where x ≠ -1/8* (My answer)
B. -12/1+8x; where x ≠ -1/8, 0
C. -12/9x; where x ≠ 0
D. -12/9

Are my answers correct?

Answer 1

Those were wrong. The correct answers are 1.) A & 2.) B

Hopefully this helps someone else in the future.

Answer 2

Helps if you type the questions correctly using brackets

1. x/(6x-x^2) , those brackets are essential
= x/(x(6-x))
= 1/(6-x), x ≠ 0, 6

2. -12x^4/(x^4+8x^5)
= -12x^4/(x^4(1 + 8x)
= -12/(1 + 8x) , x ≠ 0, -1/8

The essential restriction in both is x ≠ 0
that is,
in #1, if x = 0, the original is 0/0
while we get 1/6 in the final result, so they are not equal and we need the
restriction.

if x = 6, we get 6/0 in the original which is undefined
and we get 0/0 in the answer, which is actually indeterminate
so they both cannot be evaluated, and many authors don't see a need
to state that restriction , in that situation.

I would have accepted 1/(6-x) , x ≠ 0 as a correct simplification, with x≠6 as an implied restriction.