# Homework Help: Limit prove using definition

1. Jul 4, 2013

### scientifico

1. The problem statement, all variables and given/known data
Hello, I have to prove, using the limit definition, that $\lim_{x\to 1^{+}}{\frac{x-3}{x-1}}=-\infty$

3. 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

2. Jul 4, 2013

### 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?

3. Jul 4, 2013

### 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 $1<x<1+\frac{2}{M+1}$

4. Jul 4, 2013

### Curious3141

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