solve: 27/x - 27/x-5 = 3/x?

it might be x = -5
Not sure.

27/x - 27/(x - 5) = 3/x
9/x - 9/(x - 5) = 1/x
8/x = 9/(x - 5)
9x = 8(x - 5)
9x = 8x - 40
x = - 40

Answer: x = - 40

Proof:
(27/ - 40) - 27/(- 40 - 5) = 3/- 40
- 27/40 + 27/45 = - 3/40
- 243/360 + 216/360 = - 3/40
- 27/360 = - 3/40
(- 27/9)/(360/9) = - 3/40
- 3/40 = - 3/40

I suspect that question is incorrectly presented and SHOULD read as :-

27/x - 27 / ( x - 5 ) = 3/x

27 ( x - 5 ) - 27 x = 3 ( x - 5 )

27 x - 135 - 27 x = 3 x - 15

- 120 = 3 x

x = - 40

27/x - 27/x-5 = 3/x
=>(27(x-5)-27x)/x(x-5)) = 3/x
=>(27x-135-27x)/x(x-5))=3/x
=> -135x=3(x(x-5))
=> -135x=3(x"-5x)
=> -135x=3x"-15x
=>3x"+120x=0
=>3x(x+40)=0
=>3x=0, x+40=0
=>x=0 or x= - 40 .This is your answer!!!

27/x - 27/(x - 5) = 3/x
27/x - 3/x - 27/(x - 5) = 0
24/x - 27/(x - 5) = 0
x(x - 5)[24/x - 27/(x - 5)] = 0
24(x - 5) - 27x = 0
24*x - 24*5 - 27x = 0
24x - 27x = 120
-3x = 120
x = 120/(-3)
x = -40

27(x-5) - 27(x) = 3(x-5)

27x - 5*27 - 27x = 3x-3*5

5*27 = 3x-3*5

24*5 = 3x

x = (24*5)/3 = 40