Question

Determine the limit:
\[\frac{\frac{1}{a}-\frac{1}{x+a}}{x}, a \epsilon R\]

I tried combining the fractions to get \[\frac{x}{a(a+x)}\] in the denominator.

Answer 1

cross multiply in numerator and tell me what u get.

Answer 2

limit as \(x\to 0\) ?

Answer 3

Sorry, yes.

Answer 4

algebra
subtract in the numerator, which think is what
@hartnn meant by "cross multiply

Answer 5

yes, i meant that only.

Answer 6

you have the answer above, but don't forget there is an additional \(x\) in the denominator, which cancels with the \(x\) in the numerator

Answer 7

and u get x/a(a+x) in numerator
and x in denominator.
so the x's gets cancelled and u can directly put x=0 in remaining fraction.

Answer 8

Thanks guys!