Can't find this limit analytically

(((1/(x+1))-(1/4))/(x-3)

I need to find the limit as x approaches 3. I've simplified it to a number of other forms, but I can't get it into a form where x=3 doesn't equate to an undefined value. I know that the answer is -(1/16). Can anyone help point me in the right direction?

Re: Can't find this limit analytically

Quote:

Originally Posted by

**Diogenes** (((1/(x+1))-(1/4))/(x-3)

I need to find the limit as x approaches 3. I've simplified it to a number of other forms, but I can't get it into a form where x=3 doesn't equate to an undefined value. I know that the answer is -(1/16). Can anyone help point me in the right direction?

That fraction reduces to

Re: Can't find this limit analytically

Quote:

Originally Posted by

**Diogenes** (((1/(x+1))-(1/4))/(x-3)

I need to find the limit as x approaches 3. I've simplified it to a number of other forms, but I can't get it into a form where x=3 doesn't equate to an undefined value. I know that the answer is -(1/16). Can anyone help point me in the right direction?

start by simplifying the complex fraction ...

Re: Can't find this limit analytically

Whenever you see a problem like this, try to simplify it to a rational function (quotient of two polynomials, such as , using various strategies like common denominators, etc. Then pull out any common factors. (You may need to find the roots.)

Re: Can't find this limit analytically

Quote:

Originally Posted by

**Plato** That fraction reduces to

Quote:

Originally Posted by

**skeeter** start by simplifying the complex fraction ...

Quote:

Originally Posted by

**SworD** Whenever you see a problem like this, try to simplify it to a rational function (quotient of two polynomials, such as

, using various strategies like common denominators, etc. Then pull out any common factors. (You may need to find the roots.)

Thank you all very much. I feel stupid now, but I think I got it. Could you tell me if this reasoning is correct?

= = =

Re: Can't find this limit analytically