Question 1022059
{{{(4/(x-2))((x+2)/(x+2))-(6/(x+2))((x-2)/(x-2))=((x-2)(x+2))/((x-2)(x+2))}}}
{{{(4(x+2)-6(x-2))/(x^2-4)=(x^2-4)/(x^2-4)}}}
So then isolating the numerator,
{{{4x+8-6x+12=x^2-4}}}
{{{-2x+20=x^2-4}}}
{{{x^2+2x-24=0}}}
{{{(x+6)(x-4)=0}}}
Two solutions:
{{{x+6=0}}}
{{{x=-6}}}
and
{{{x-4=0}}}
{{{x=4}}}
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Graphical verification
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*[illustration fq7.JPG].