# How do you find the limit of #((1/x+16)-(1/16)) / x# as x approaches 0?

##### 1 Answer

I think you meant:

When we try to find the limit, we get the (indeterminate) form

The important algebra can be done in a couple ways:

**Method 1**

"If I had a fraction over a fraction, I'd know what to do next."

Good! Make it so.

#= ((16- (x+16))/(16(x+16)))/(x/1)#

#= (-x)/(16(x+16))*1/x#

#= (-1)/(16(x+16))#

**Method 2**

"I know this trick:"

Multiply numerator and denominator by the common denominator of all the fractions in the numerator and denominator. (Sounds complicated, but it's quicker.)

The common denominator is

#= ((16(x+16))/(x+16) - (16(x+16))/16)/(x(16(x+16))#

#=(16-(x+16))/(16x(x+16))#

#= (-1)/(16(x+16))#

**So, we get:**