((x)/(x+2))+((5)/(x-3))=(25)/(x^2-x-6)

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Solution for ((x)/(x+2))+((5)/(x-3))=(25)/(x^2-x-6) equation: 


D( x )

x^2-x-6 = 0

x+2 = 0

x-3 = 0

x^2-x-6 = 0

x^2-x-6 = 0

x^2-x-6 = 0

DELTA = (-1)^2-(-6*1*4)

DELTA = 25

DELTA > 0

x = (25^(1/2)+1)/(1*2) or x = (1-25^(1/2))/(1*2)

x = 3 or x = -2

x+2 = 0

x+2 = 0

x+2 = 0 // - 2

x = -2

x-3 = 0

x-3 = 0

x-3 = 0 // + 3

x = 3

x in (-oo:-2) U (-2:3) U (3:+oo)

x/(x+2)+5/(x-3) = 25/(x^2-x-6) // - 25/(x^2-x-6)

x/(x+2)+5/(x-3)-(25/(x^2-x-6)) = 0

x/(x+2)+5/(x-3)-25*(x^2-x-6)^-1 = 0

x/(x+2)+5/(x-3)-25/(x^2-x-6) = 0

x^2-x-6 = 0

x^2-x-6 = 0

x^2-x-6 = 0

DELTA = (-1)^2-(-6*1*4)

DELTA = 25

DELTA > 0

x = (25^(1/2)+1)/(1*2) or x = (1-25^(1/2))/(1*2)

x = 3 or x = -2

(x+2)*(x-3) = 0

x/(x+2)+5/(x-3)-25/((x+2)*(x-3)) = 0

(x*(x-3))/((x+2)*(x-3))+(5*(x+2))/((x+2)*(x-3))-25/((x+2)*(x-3)) = 0

x*(x-3)+5*(x+2)-25 = 0

x^2+2*x-25+10 = 0

x^2+2*x-15 = 0

x^2+2*x-15 = 0

x^2+2*x-15 = 0

DELTA = 2^2-(-15*1*4)

DELTA = 64

DELTA > 0

x = (64^(1/2)-2)/(1*2) or x = (-64^(1/2)-2)/(1*2)

x = 3 or x = -5

(x+5)*(x-3) = 0

((x+5)*(x-3))/((x+2)*(x-3)) = 0

((x+5)*(x-3))/((x+2)*(x-3)) = 0 // * (x+2)*(x-3)

(x+5)*(x-3) = 0

( x+5 )

x+5 = 0 // - 5

x = -5

( x-3 )

x-3 = 0 // + 3

x = 3

x in { 3} 

x = -5

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