Simplify x / 6x - x^2

Question

Please show me how you did it so i can understand!

Another one, Simplify x^2 - 3x - 18 / x + 3
This is a fraction

Another one, k + 3 / 4k - 2 (this is a fraction) * 12k^2 + 2k - 4)

Answer 1

x/(6x-x^2)
= x / x(6-x)
= 1/(6-x)

(x^2 - 3x - 18) / (x + 3)
= (x-5)(x+3)/(x+3)
= x-5

(k+3)/(4k-2) * (12k^2+2k-4)
= (k+3)/(2(2k-1)) * 2(2k-1)(3k+2)
= (k+3)/(3k+2)

Answer 2

for 1 and 3, they are right, but for 2, the answer choices are
x-3,
x-6 where x doesn't equal -3
and x-6 where x doesn't equal 6

Answer 3

for #2, Steve meant to say:

(x-6)(x+3)/(x+3)
= x-6 , x ≠ -3

Answer 4

Yes, I neglected to mention excluded values. One cannot gloss over stuff like that. My bad.

Answer 5

It's okay! XD You both did a good job showing me how its done!