Question #bb82d

1 Answer
Jim H · cspark1981
Oct 15, 2015

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#.

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