How can I use this hint to help prove the limit using the definition?

[scientifico]

Homework Statement

Hello, I have to prove, using the limit definition, that \lim_{x\to 1^{+}}{\frac{x-3}{x-1}}=-\infty

The Attempt at a Solution

I've set this unequation \frac{x-3}{x-1} < - M but it doesn't lead to the result 1<x<1+\frac{2}{M+1}, what did I wrong ?

Thanks

 

[HallsofIvy]

You do understand that we can't tell you what you did wrong if you don't tell us what you did, don't you?

 

[scientifico]

I've set up this unequation \frac{x-3}{x-1} < - M to prove the limit using its definition but it doesn't lead to the result 1<x<1+\frac{2}{M+1}

 

[Curious3141]

I've set up this unequation \frac{x-3}{x-1} < - M to prove the limit using its definition but it doesn't lead to the result 1<x<1+\frac{2}{M+1}

Hint: $M+3 = (M+1) + 2$.