(-8/(x-5))-(2/(x+2))=3

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Solution for (-8/(x-5))-(2/(x+2))=3 equation: 


D( x )

x-5 = 0

x+2 = 0

x-5 = 0

x-5 = 0

x-5 = 0 // + 5

x = 5

x+2 = 0

x+2 = 0

x+2 = 0 // - 2

x = -2

x in (-oo:-2) U (-2:5) U (5:+oo)

-8/(x-5)-(2/(x+2)) = 3 // - 3

-8/(x-5)-(2/(x+2))-3 = 0

-8/(x-5)-2*(x+2)^-1-3 = 0

-8/(x-5)-2/(x+2)-3 = 0

(-8*(x+2))/((x-5)*(x+2))+(-2*(x-5))/((x-5)*(x+2))+(-3*(x-5)*(x+2))/((x-5)*(x+2)) = 0

-8*(x+2)-2*(x-5)-3*(x-5)*(x+2) = 0

9*x-3*x^2-10*x-6+30 = 0

24-3*x^2-x = 0

24-3*x^2-x = 0

24-3*x^2-x = 0

DELTA = (-1)^2-(-3*4*24)

DELTA = 289

DELTA > 0

x = (289^(1/2)+1)/(-3*2) or x = (1-289^(1/2))/(-3*2)

x = -3 or x = 8/3

(x+3)*(x-8/3) = 0

((x+3)*(x-8/3))/((x-5)*(x+2)) = 0

((x+3)*(x-8/3))/((x-5)*(x+2)) = 0 // * (x-5)*(x+2)

(x+3)*(x-8/3) = 0

( x+3 )

x+3 = 0 // - 3

x = -3

( x-8/3 )

x-8/3 = 0 // + 8/3

x = 8/3

x in { -3, 8/3 }

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