The discussion revolves around evaluating the limit of a quotient involving rational functions as x approaches 3. The specific limit in question is (1/x - 1/3) / (x-3).
Some participants offer guidance on finding a common denominator for the fractions in the numerator and suggest simplifying the expression further. Multiple interpretations of the problem are being explored, particularly regarding the handling of the limit and the algebra involved.
There is mention of confusion regarding the simplification process and the need for clarity in handling the fractions involved. The original poster expresses uncertainty about the top part of the expression.
Combine the two fractions in the numerator, and then simplify. This problem isn't much more than an exercise in working with fractions.Alice7979 said: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.