Question 1208445
If {{{x<>2}}} and {{{X<>-1/8}}} then {{{x-2<>0}}} and {{{8x+1<>0}}} .
In that case, multiplying numerator and denominator of a fraction times those expressions results in a fraction that is equivalent for all considered values of {{{x}}} .
{{{(8x + 1)^"1/3"/((3(x - 2))^"1/2")^"1/3")}}} {{{"+"}}} {{{((x - 2)^"1/3")/((24(8x + 1))^"1/2")^"1/3"}}}{{{"="}}} {{{(8x + 1)^"1/3"/((3^"1/3")(x - 2)^"1/6"))}}} {{{"+"}}} {{{((x - 2)^"1/3")/((3^"1/3")(8^"1/3")(8x + 1)^"1/6"))}}}{{{"="}}} {{{(8x + 1)^"1/3"/((3^"1/3")(x - 2)^"1/6"))}}} {{{"+"}}} {{{((x - 2)^"1/3")/(2(3^"1/3")(8x + 1)^"1/6"))}}}
 
{{{"="}}} {{{(2(8x + 1)^"1/3"(8x + 1)^"1/6")/
(2(3^"1/3")(x - 2)^"1/6"(8x + 1)^"1/6"))}}} {{{"+"}}} {{{((x - 2)^"1/3"(x - 2)^"1/6")/(2(3^"1/3")(x - 2)^"1/6"(8x + 1)^"1/6"))}}}
 
{{{"="}}} {{{(2(8x + 1)^"1/3+1/6")/
(2(8x^2-15x-2)^"1/6")}}} {{{"+"}}} {{{((x - 2)^"1/3+1/6")/(2(8x^2-15x-2)^"1/6")}}}{{{"="}}} {{{(2(8x + 1)^"1/2")/
(2(8x^2-15x-2)^"1/6")}}} {{{"+"}}} {{{((x - 2)^"1/2")/(2(8x^2-15x-2)^"1/6")}}}{{{"="}}} {{{(2(8x + 1)^"1/2"+(x - 2)^"1/2")/
(2(8x^2-15x-2)^"1/6")}}}
 
{{{"="}}} {{{(2sqrt(8x + 1)+sqrt(x - 2))/
(2root(6,(8x^2-15x-2)))}}}