## anonymous one year ago lim(x->1) (sqrt(x)-1)/(x-1) I know the answer but not how to get to that answer.

1. anonymous

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2. anonymous

please re post the question correctly

3. anonymous

Exactly how do I do that?

4. Michele_Laino

hint, we can write this: $\Large \frac{{\sqrt x - 1}}{{x - 1}} = \frac{{\sqrt x - 1}}{{\left( {\sqrt x + 1} \right)\left( {\sqrt x - 1} \right)}}$

5. anonymous

If I have to complexly program my text to be easily understandable, instead of simply being able to draw it for you, then I think I will take my leave.

6. anonymous

just watch and learn. if you leave , you lose

7. Michele_Laino

if we simplify my expression above, we get this: $\Large \frac{{\sqrt x - 1}}{{x - 1}} = \frac{{\sqrt x - 1}}{{\left( {\sqrt x + 1} \right)\left( {\sqrt x - 1} \right)}} = \frac{1}{{\sqrt x + 1}}$ and the rightmost side is a continuous function at x=1 @Xep

8. anonymous

The main thing I don't understand is how to do that first step (which I assume is conjugation)

9. Michele_Laino

no, it is the application of this factorization: $\Large {a^2} - {b^2} = \left( {a + b} \right)\left( {a - b} \right)$

10. Michele_Laino

where a^2 = x, and b^2=1

11. anonymous

Oh I see it now, thanks for helping it click for me :)

12. Michele_Laino

:)