(1)/(x-4)+1=(14)/(x+2)

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Solution for (1)/(x-4)+1=(14)/(x+2) equation: 


D( x )

x+2 = 0

x-4 = 0

x+2 = 0

x+2 = 0

x+2 = 0 // - 2

x = -2

x-4 = 0

x-4 = 0

x-4 = 0 // + 4

x = 4

x in (-oo:-2) U (-2:4) U (4:+oo)

1/(x-4)+1 = 14/(x+2) // - 14/(x+2)

1/(x-4)-(14/(x+2))+1 = 0

1/(x-4)-14*(x+2)^-1+1 = 0

1/(x-4)-14/(x+2)+1 = 0

(1*(x+2))/((x-4)*(x+2))+(-14*(x-4))/((x-4)*(x+2))+(1*(x-4)*(x+2))/((x-4)*(x+2)) = 0

1*(x+2)-14*(x-4)+1*(x-4)*(x+2) = 0

x^2-13*x-2*x-8+58 = 0

x^2-15*x+50 = 0

x^2-15*x+50 = 0

x^2-15*x+50 = 0

DELTA = (-15)^2-(1*4*50)

DELTA = 25

DELTA > 0

x = (25^(1/2)+15)/(1*2) or x = (15-25^(1/2))/(1*2)

x = 10 or x = 5

(x-5)*(x-10) = 0

((x-5)*(x-10))/((x-4)*(x+2)) = 0

((x-5)*(x-10))/((x-4)*(x+2)) = 0 // * (x-4)*(x+2)

(x-5)*(x-10) = 0

( x-10 )

x-10 = 0 // + 10

x = 10

( x-5 )

x-5 = 0 // + 5

x = 5

x in { 10, 5 }

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