Solve the rational equation 1/n-4 - 2/n = 3/4-n

n=4

Step-by-step explanation:

Given equation: \[\frac{1}{n-4}-\frac{2}{n}=\frac{3}{4-n}\]

Simplifying the Left Hand Side of the equation by taking the LCM of the denominator terms:

\[\frac{n}{n*(n-4)}-\frac{2*(n-4)}{n*(n-4)}=\frac{3}{4-n}\]

=> \[\frac{n - 2*(n-4)}{n*(n-4)}=\frac{3}{4-n}\]

=> \[\frac{n - 2n + 8}{n*(n-4)}=\frac{3}{4-n}\]

=> \[\frac{8 - n}{n*(n-4)}=\frac{3}{4-n}\]

=> \[(8-n)*(4-n) =n*(n-4)*3\]

=> \[n-8 =3n\]

=> \[2n =8\]

=> n = 4