Question 1107712
<pre>
{{{matrix(2,3,"","","",

x^(5/7),""-"",x^(1/7))}}}

Let {{{matrix(2,3,"","","",

u,""="",x^(1/7))}}}, then {{{matrix(2,5,"","","","","",

x^(5/7),""="",(x^(1/7))^(""^5),""="",u^5)}}},

So now,

{{{matrix(2,3,"","","",

x^(5/7),""-"",x^(1/7))}}} becomes

{{{matrix(1,3,u^5,""-"",u)}}}

Factor out u:

{{{matrix(1,3,"u(u"^4,""-"","1)")}}}

We factor u<sup>4</sup>-1 as the difference of two squares:

{{{u(u^2-1)(u^2+1)}}}

We factor u<sup>2</sup>-1 as the difference of two squares:

{{{u^""(u^""-1)(u^""+1)(u^2+1)}}}

Now we replace all the u's by x<sup>1/7</sup>


{{{matrix(2,1,"",


x^(1/7)(x^(1/7)-1)(x^(1/7)+1)((x^(1/7))^2+1))}}}

Multiply exponents in the last parentheses:


{{{matrix(2,1,"",


x^(1/7)(x^(1/7)-1)(x^(1/7)+1)(x^(2/7)+1))}}}

Edwin</pre>