((x-5)/2)+(2/(x+5))=(13/2)

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Solution for ((x-5)/2)+(2/(x+5))=(13/2) equation: 


D( x )

x+5 = 0

x+5 = 0

x+5 = 0

x+5 = 0 // - 5

x = -5

x in (-oo:-5) U (-5:+oo)

(x-5)/2+2/(x+5) = 13/2 // - 13/2

(x-5)/2+2/(x+5)-(13/2) = 0

(x-5)/2+2/(x+5)-13/2 = 0

((x-5)*(x+5))/(2*(x+5))+(2^2)/(2*(x+5))+(-13*(x+5))/(2*(x+5)) = 0

(x-5)*(x+5)-13*(x+5)+4 = 0

x^2-13*x-65-21 = 0

x^2-13*x-86 = 0

x^2-13*x-86 = 0

x^2-13*x-86 = 0

DELTA = (-13)^2-(-86*1*4)

DELTA = 513

DELTA > 0

x = (513^(1/2)+13)/(1*2) or x = (13-513^(1/2))/(1*2)

x = (3*57^(1/2)+13)/2 or x = (13-3*57^(1/2))/2

(x-((13-3*57^(1/2))/2))*(x-((3*57^(1/2)+13)/2)) = 0

((x-((13-3*57^(1/2))/2))*(x-((3*57^(1/2)+13)/2)))/(2*(x+5)) = 0

((x-((13-3*57^(1/2))/2))*(x-((3*57^(1/2)+13)/2)))/(2*(x+5)) = 0 // * 2*(x+5)

(x-((13-3*57^(1/2))/2))*(x-((3*57^(1/2)+13)/2)) = 0

( x-((13-3*57^(1/2))/2) )

x-((13-3*57^(1/2))/2) = 0 // + (13-3*57^(1/2))/2

x = (13-3*57^(1/2))/2

( x-((3*57^(1/2)+13)/2) )

x-((3*57^(1/2)+13)/2) = 0 // + (3*57^(1/2)+13)/2

x = (3*57^(1/2)+13)/2

x in { (13-3*57^(1/2))/2, (3*57^(1/2)+13)/2 }

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