Question 1171633
<pre>
{{{ x/(x+5) - 5/(x-5) = 14 }}}

Multiply both sides by (x+5)(x-5), and you get:
{{{  x(x-5) - 5(x+5) = 14(x+5)(x-5) }}}

Combine & simplify (steps shown):
{{{  (x^2-5x) - (5x+25) = 14(x^2-25) }}}
{{{  x^2-10x-25 = 14x^2-350 }}}
{{{ 13x^2+10x-325 = 0 }}}

Here I just used the quadratic formula:  for {{{ax^2 + bx + c = 0 }}}, you get 
 {{{ x = (1/(2a))(-b +- sqrt(b^2-4ac)) }}}


{{{ x = (1/(2*13))( -10 +-sqrt(100-4(13)(-325))) }}}

{{{ x = (1/(2*13))( -10 +-sqrt(100*170))) }}}
{{{ x = (1/(2*13))( -10 +- 10*sqrt(170))) }}}
{{{ highlight( x = (5/13)( -1 +-sqrt(170))))  }}}   <--- exact answer
 

Approximate answer:
{{{ x=-5.399336 }}}
and
{{{ x=4.630156 }}}

Plug in these values for x and you will see they both result in approx 14.