Question 988368
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{{{x/(x-3) + 4/(x+5)=8x/((x-3)(x+5))}}} Multiply each side by (x-3).
{{{x+(4(x-3))/(x+5)=(8x)/(x+5)}}} Multiply each side by (x+5).
{{{(x)(x+5)+(4)(x-3)=8x}}}
{{{x^2+5x+4x-12=8x}}} Subtract 8x from each side.
{{{x^2+x-12=0}}}
{{{(x+4)(x-3)=0}}}
{{{x+4=0}}} {{{OR}}} {{{x-3=0}}}
{{{x=-4}}} {{{OR}}} {{{x=3}}}
From the domain of the original equation, we know xdoes not equal 3 or -5
(that would cause division by zero),so we are left with:
ANSWER: x=-4 
You can check by putting the value in the original equation:
Negative 4 works, positive four does not, 
so there is an error in your book.
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CHECK:
For x=4:
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{{{x/(x-3) + 4/(x+5)=8x/((x-3)(x+5))}}}
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{{{4/(4-3)+4/(4+5)=(8(4))/((4-3)(4+5))}}}
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{{{4/1+4/9=32/9}}}
{{{36/9+4/9=32/9}}}
{{{40/9=32/9}}} False, so 4 is NOT a solution.
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For x=-4:
{{{x/(x-3) + 4/(x+5)=8x/((x-3)(x+5))}}}
{{{-4/(-4-3)+4/(-4+5)=(8(-4))/((-4-3)(-4+5))}}}
{{{(-4/-7)+4=(-32/-7)}}}
{{{4/7)+(28/7)=32/7}}}
{{{32/7=32/7}}} True, -4 IS our solution.