The limit problem presented involves evaluating the expression lim (1/x - 1/3) / (x-3) as x approaches 3. The correct solution is -1/9, achieved by combining the fractions in the numerator and simplifying rather than attempting to cancel (x-3) directly. The confusion arises from the 0/0 indeterminate form, which can be resolved by finding a common denominator for the fractions in the numerator. This approach is essential for correctly applying the Quotient Law in calculus.
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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.