Question 342387
First simpify,
{{{(x+4)/(x+2)=7/(x+2) + 24/(x^2-4)}}}
{{{(x+4-7)/(x+2)-24/(x^2-4)=0}}}
{{{(x-3)/(x+2)-24/(x^2-4)=0}}}
Use the common denominator, {{{x^2-4=(x-2)(x+2)}}}
{{{(x-3)/(x+2)= ((x-3)(x-2))/((x-2)(x+2))
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{{{((x-3)(x-2))/((x-2)(x+2))-24/(x^2-4)=0}}}
{{{(x^2-2x-3x+6-24)/((x-2)(x+2))=0}}}
{{{(x^2-5x-18)/((x-2)(x+2))=0}}}
Find the zeros of the numerator using the quadratic formula,
{{{x = (5 +- sqrt( (5)^2-4*1*(-18) ))/(2*1) }}}
{{{x = (5 +- sqrt( 25+72))/2 }}}
{{{highlight(x = (5 +- sqrt( 79))/2) }}}