Question 643999
<pre>
{{{x/(x^2-100)}}} + {{{7/x}}}

Factor x²-100 as (x-10)(x+10)

{{{x/((x-10)(x+10))}}} + {{{7/x}}}

The LCD is x(x-10)(x+10)

Multiply the first fraction by {{{x/x}}} since that is the only
factor of the LCD which the first fraction's denominator does not contain.

Multiply the first fraction by {{{((x-10)(x+10))/((x-10)(x+10))}}} since they are the factors 
of the LCD which the second fraction's denominator does not contain.

{{{x/x}}}·{{{x/((x-10)(x+10))}}} + {{{((x-10)(x+10))/((x-10)(x+10))}}}·{{{7/x}}}

{{{x^2/(x(x-10)(x+10))}}} + {{{(7(x-10)(x+10))/(x(x-10)(x+10))}}}

Multiply out the right numerator (not the denominator)

{{{x^2/(x(x-10)(x+10))}}} + {{{(7(x^2-100))/(x(x-10)(x+10))}}}

{{{x^2/(x(x-10)(x+10))}}} + {{{(7x^2-700))/(x(x-10)(x+10))}}}

Combine both numerators over the LCD:

{{{(x^2+7x^2-700)/((x-10)(x+10))}}}

{{{(8x^2-700)/(x(x-10)(x+10))}}}

Since you want everything factored completely,
 factor out 4 in the top:

{{{(4(2x^2-175))/(x(x-10)(x+10))}}}

Edwin</pre>