Finding the Limit: (1/(x-1)) - (2/(x^2-1))

[syd9231]

Homework Statement

Find the following limit

lim (1/(x-1))-(2/(x^2-1))
x→0

Homework Equations

The Attempt at a Solution

I tried simplifying the equation into one fraction by finding a common denominator. I did this to try to get a denominator where I could plug 1 in without it equaling 0. It didn't work, i ended up with (x^2-2x)/(x^3-x^2-x+1). I feel like I went in the wrong direction from the beginning. If someone could tell me what detail I'm missing it would be greatly appreciated! Thanks!

 

[Mark44]

Homework Statement

Find the following limit

lim (1/(x-1))-(2/(x^2-1))
x→0

Homework Equations

The Attempt at a Solution

I tried simplifying the equation into one fraction by finding a common denominator. I did this to try to get a denominator where I could plug 1 in without it equaling 0. It didn't work, i ended up with (x^2-2x)/(x^3-x^2-x+1).

The LCD is x² -1, not (x - 1) (x² - 1). All you need to do is multiply the first fraction by x + 1 over itself.

I feel like I went in the wrong direction from the beginning. If someone could tell me what detail I'm missing it would be greatly appreciated! Thanks!

 

[syd9231]

I did that which left me with (x - 1)/(x^2 - 1) but that still makes the expression undefined when I input 1. I know the answer is 1/2, but I still don't see it. Does the expression mean 1/2 and I'm missing it or is there more computation involved?

 

[Mark44]

There's a little bit more to do. Factor the denominator and cancel the common factors in top and bottom.