Question 558801
{{{2x/(x^2-16)-2/(x-4)=4/(x+4)}}}
{{{2x/(x^2-16)=4/(x+4)+2/(x-4)}}}
Take LCD on L.H.S
{{{2x/(x^2-16)=(4(x-4)+2(x+4))/(x+4)(x-4)}}}
{{{2x/(x^2-16)=(4(x-4)+2(x+4))/(x^2-4x+4x-16)}}}
{{{2x/(x^2-16)=(4x-16+2x+8)/(x^2-cross(4x)+cross(4x)-16)}}}
{{{2x/(x^2-16)=(6x-8)/(x^2-16)}}}
{{{2x/cross(x^2-16)=(6x-8)/cross(x^2-16)}}}
{{{2x=6x-8}}}
{{{2x-6x=-8}}}
{{{-4x=-8}}}
Divide by -4 both sides of above equation
{{{-4x/-4=-8/-4}}}
{{{cross(-4x)/cross(-4)=cross(-8)/cross(-4)}}}

{{{x=2}}}


Check
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{{{2x/(x^2-16)-2/(x-4)=4/(x+4)}}}
Put x=2
{{{2(2)/((2)^2-16)-2/(2-4)=4/(2+4)}}}
{{{4/(4-16)-2/-2=4/6}}}
{{{(4/-12)-(2/-2)=4/6}}}
{{{(cross(4)/cross(-12))-(cross(2)/cross(-2))=cross(4)/cross(6)}}}
{{{(-1/3)+1=2/3}}}
{{{(-1+3)/3=2/3}}}
{{{2/3=2/3}}}