What is 1/2n^2+5/2n=n-2/n^2?

Question

I am trying to figure out the steps to get -5/3 but I keep coming up with 15. Does anyone know a different way.

Answer 1

1/2n^2+5/2n=n-2/n^2
(1+5n)/2n^2=n-2/n^2
n^2(1+5n)=2n^2(n-2)
n^2+5n^3=2n^3-4n^2
n^2+4n^2=2n^3-5n^3
5n^2= -3n^3
n^3/n^2=5/-3
n= -5/3

Answer 2

Without brackets, the question can read a number of different ways.
Will take a guess and go for:-

1 / (2 n ²) + 5 / (2 n) = (n - 2) / n ²
1 + 5 n = 2 (n - 2)
1 + 5 n = 2 n - 4
3 n = - 5
n = - 5 / 3

Answer 3

1/2n^2+5/2n=n-2/n^2
Taking lcm of left hand side as 2n^2
(1+5n) /2n^2 = (n-2 )/n^2
1+5n =2( n-2)
1+5n = 2n-4
5n-2n= -4-1
3n = -5
n= -5/3