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.

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.

hartnn · Answer

cross multiply in numerator and tell me what u get.

anonymous · Answer

limit as $x\to 0$ ?

anonymous · Answer

Sorry, yes.

anonymous · Answer

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

hartnn · Answer

yes, i meant that only.

anonymous · Answer

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

hartnn · Answer

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.

anonymous · Answer

Thanks guys!