Question

Solve the equation for x. For each of the following problems is it possible for x to be equal to: 1?

(x+m)/(x−1)=1

If m ≠ -1, there are no solutions\

if m=1, the solution is ?
Ii do not now how to find the solution for if m=1 but i got all real numbers, but my teacher says that it is wrong

Answer 1

If m=1, you have

(x+1)/(x-1) = 1
x+1 = x-1
1 = -1

So, there is no solution, as you already noted.

This is made clear when you solve for x:

(x+m)/(x−1)=1
x+m = x-1
m = -1

That is the only value of m which works.

Answer 2

I agree, unless you also use m = i^2 where i = sqrt(-1)

There is no possible solution for m =+1.