Question 185755
<pre><font size = 4 color = "indigo"><b>

{{{ 2/x = x/(x^2-8) }}}

Enclose both sides in parentheses:

{{{ (2/x) = (x/(x^2-8)) }}}

Multiply both sides by the LCD of {{{x*(x^2-8)}}}

{{{ x*(x^2-8)(2/x) = x*(x^2-8)(x/(x^2-8)) }}}

Then cancel:

{{{ cross(x)*(x^2-8)(2/cross(x)) = x*(cross(x^2-8))(x/(cross(x^2-8))) }}}


{{{ (x^2-8)(2) = x*(x) }}}

{{{ 2(x^2-8) = x^2 }}}

{{{2x^2-16 = x^2}}}

{{{x^2-16=0}}}

{{{(x-4)(x+4)=0}}}

{{{x-4=0}}}  {{{x+4=0}}}
{{{x=4}}}    {{{x=-4}}}

Two solutions. Both check.

Edwin</pre>