Question

Question #bb82d

Answer 1

If you are trying to find `lim_(xrarra)( x^(1/m) - a^(1/m) )/(x-a)`, see the explanation section.

Explanation:

I'm going to guess that this is what you mean by "solve".
If that's correct, we use

`u^m-v^m = (u-v)(u^(m-1) + u^(m-2)v + u^(m-3)v + * * * uv^(m-2)+v^(m-1))`

With `u = x^(1/m)` and `v=a^(1/m)` we can either factor the denominator

`x-a=(x^(1/m))^m - (a^(1/m))^m = ( x^(1/m) - a^(1/m) )(x^((m-1)/m) + x^((m-2)/ma^(1/m)+ * * * + a^((m-1)/m) ))`

Or multiply by `(x^((m-1)/m) + x^((m-2)/ma^(1/m)+ * * * + a^((m-1)/m)))/ (x^((m-1)/m) + x^((m-2)/ma^(1/m)+ * * * + a^((m-1)/m) )` to make the numerator `x-a`.