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

Staff Emeritus
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: $M+3 = (M+1) + 2$.

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