Limits question ((x+1)/(x-1)-3)/(x-2)

[venger]

Homework Statement

F(x) = [x+1 / x-1] coordinates (2,3)

Homework Equations

First principle Mtang=(F(x)-F(a))/x-a
second principle
finding the derivatives at first glance

The Attempt at a Solution

Mtang=(F(x)-F(a))/x-a
[x+1/x-1]-(3)/(x-2)
Multiply by (x-1/x-1) to get
x+1 - 3(x-1)
----------- <- over (fraction)
(x-2)(x-1)
<<
x+1-3
---------- <- Over (fraction)
(x-2)
<<
x-2
-----
x-2

equals ONE!

 

[Werg22]

Are you familiar with l'Hôpital's rule?

 

[venger]

No I am not

 

[Dick]

Check your algebra going from the first 'over (fraction)' to the second one. You somehow made x-1 'disappear' through use of bad algebra. Simplify the numerator in the first expression.

 

[venger]

Thats okay i know what to do know, 3x divided by x is 2x

 

[Dick]

Thats okay i know what to do know, 3x divided by x is 2x

3x MINUS x is 2x. 3x divided by x is 3. Are you sure you know what to do?

 

[venger]

well forget about it i got a tutor now

 

[Dick]

Good luck!

 

[Werg22]

Meh, IMO, a tutor can only have a negative impact.

 

[Gib Z]

How do we have a better impact than a tutor :S

 

[Werg22]

We don't but it doesn't exclude the fact that a tutor doesn't, IMO.

 

[drpizza]

How do we have a better impact than a tutor :S

Because we're doing it because we love mathematics and enjoy helping others. The tutor is doing it to make money, or because it's a required work-study job.

 

[Gib Z]

Lol Thats a good point, the only reason we would even be helping is because we want to, and because of that we put in our best effort. But id rather be half-assed AND get paid! :P