Question

1/n-2 - 2/2-n = 1/6
what is the value of n in this equation.jjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjj

Answer 1

solution:
1/n-2 -2/2-n =1/6
1/n-2 -2/2-n
by Cross multiplication we get
1(2-n) -2(n-2)/(n-2)(2-n) = 1/6
(2-n -2n +4 ) / (n-2)(2-n) = 1/6
(6 - 3n )/(n-2)(2-n) = 1/6
by cross multiplication we get
6(6-3n) = (n-2)(2-n)
36 - 18n = n(2-n)-2(2-n)
36 -18n = 2n -n^2 -4 +2n
36 -18n=4n - n^2 - 4
36 - 18n - 4n +n^2 +4 = 0
(36+4) - (18n+4n) + n^2 = 0
40 - 22n + n^2 = 0
n^2 - 22n + 40 = 0
n^2 - 2n - 20n +40 =0
n(n - 2 ) - 20 ( n - 2 ) = 0
(n - 20 )(n - 2) = 0
Either  ( n - 20 ) = 0 or n -2 = 0
=> n=20 or n= 2
Hope this helps You