What is the value of m when the equation X-2 / 2 + X-2 / 4 MX = 0 has no solution?

What is the value of m when the equation X-2 / 2 + X-2 / 4 MX = 0 has no solution?

2/(X-2)+mx/(X^2-4)=0
2(x+2)/(x^-4)+mx/(x^2-4)=0
2 (x + 2) + MX = 0 and X ≠ ± 2
x=-4/(m+2)
Satisfy no solution M = - 2

If the fractional equation XX − 3 − 2 = MX − 3 has no solution, then the value of M is______ ．

If we remove the denominator, we get x-2x + 6 = m, and substitute x = 3 to get: - 3 + 6 = m, then M = 3

Solve the equation about X, x ^ 2 + MX + 2 = MX ^ 2 + 3x (where m ≠ 1)
Additional within 2 hours

(m-1)x^2+(3-m)x-2=0
Discriminant = (3-m) ^ 2 + 8 (m-1) = m ^ 2-6m + 9 + 8m-8 = m ^ 2 + 2m + 1 = (M + 1) ^ 2
So x = [- (3-m) ± (M + 1)] / [2 (m-1)]
-(3-m)+(m+1)=2m-2=2(m-1)
-(3-m)-(m+1)=2
So X1 = 1, X2 = 1 / (m-1)