Question 990921
{{{y[1] = 2x/(x-8)}}}, {{{y[2] = 3/(x+7)}}}, 

given condition: {{{y[1] + y[2] = 1}}}


{{{2x/(x-8)+3/(x+7)=1}}}

{{{(2x(x+7)+3(x-8))/((x-8)(x+7))=1}}}

{{{2x(x+7)+3(x-8)=1(x-8)(x+7)}}}

{{{2x^2+14x+3x-24=x^2+7x-8x-56}}}

{{{2x^2+17x-24=x^2-x-56}}}

{{{2x^2+17x-24-x^2+x+56=0}}}

{{{x^2+18x+32=0}}}

{{{x^2+2x+16x+32=0}}}

{{{(x^2+2x)+(16x+32)=0}}}

{{{x(x+2)+16(x+2)=0}}}

{{{(x+2)(x+16) = 0}}}

solutions:

if {{{(x+2)= 0}}}=>{{{x=-2}}}
if {{{(x+16) = 0}}}=>{{{x=-16}}}

check:
=>{{{x=-2}}}

{{{y[1] = 2x/(x-8)}}}=>{{{y[1] = (2(-2))/(-2-8)=-4/-10=2/5}}} 
{{{y[2] = 3/(x+7)}}}=>{{{y[2] = 3/(-2+7)=3/5}}}

given condition: {{{y[1] + y[2] = 1}}}=>{{{2/5 + 3/5=5/5 = 1}}}

now you can check for =>{{{x=-16}}}