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

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

There is no possible solution for m =+1.

To solve the equation (x+m)/(x-1) = 1 when m = 1, we can start by multiplying both sides of the equation by (x-1):

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

This simplifies to:

x + m = x - 1

Next, we can subtract x from both sides of the equation:

x + m - x = x - 1 - x

This simplifies to:

m = -1

Therefore, when m = 1, the solution to the equation is x = -1.

It seems there might be a misunderstanding with your teacher. The solution x = -1 is valid when m = 1.

To solve the equation (x+m)/(x-1) = 1 for x, you can follow these steps:

1. Multiply both sides of the equation by (x-1) to eliminate the fraction:
(x+m)/(x-1) * (x-1) = 1 * (x-1)
(x+m) = x - 1

2. Expand the equation:
x + m = x - 1

3. Subtract x from both sides of the equation:
x - x + m = x - x - 1
m = -1

So, if m ≠ -1, there are no solutions to the equation. However, if m = -1, the equation becomes m = -1, which is one solution.

Now, if m = 1, let's substitute it back into the equation and solve for x:

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

To eliminate the fractions, we can cross-multiply:

x + 1 = x - 1

Subtract x from both sides:

1 = -1

This equation is not possible because both sides are not equal. Therefore, if m = 1, there is no solution to the equation. Make sure to double-check with your teacher regarding their expectations for this specific equation.

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.