How Do You Solve the Limit Using the Quotient Law?

[Alice7979]

Homework Statement

lim (1/x - 1/3) / (x-3)
x->3

Homework Equations

The Attempt at a Solution

I tried to cancel the bottom (x-3) out by multiplying the top by 3/3 and x/x and then got ((3-x)/3x)/(x-3) but ended with 0/0 and the right answer is -1/9. The top part is confusing me.

 

[fresh_42]

Why didn't you cancel $x-3\,?$ Or: how are quotients of quotients calculated?

Btw., formulas are much easier to read if you use the LaTeX interpreter: https://www.physicsforums.com/help/latexhelp/

 

[Mark44]

Homework Statement

lim (1/x - 1/3) / (x-3)
x->3

Homework Equations

The Attempt at a Solution

I tried to cancel the bottom (x-3) out by multiplying the top by 3/3 and x/x and then got ((3-x)/3x)/(x-3) but ended with 0/0 and the right answer is -1/9. The top part is confusing me.

Combine the two fractions in the numerator, and then simplify. This problem isn't much more than an exercise in working with fractions.

 

[scottdave]

Like @Mark44 said, find a common denominator between $\frac 1 x \text{ and } \frac 1 3$. Similar to if you were adding the fractions $\frac 1 7 \text{ and } \frac 1 3$