(x-4)/(5x-15)=1/(x+3)

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Solution for (x-4)/(5x-15)=1/(x+3) equation: 


D( x )

5*x-15 = 0

x+3 = 0

5*x-15 = 0

5*x-15 = 0

5*x-15 = 0 // + 15

5*x = 15 // : 5

x = 15/5

x = 3

x+3 = 0

x+3 = 0

x+3 = 0 // - 3

x = -3

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

(x-4)/(5*x-15) = 1/(x+3) // - 1/(x+3)

(x-4)/(5*x-15)-(1/(x+3)) = 0

(x-4)/(5*x-15)-(x+3)^-1 = 0

(x-4)/(5*x-15)-1/(x+3) = 0

((x-4)*(x+3))/((5*x-15)*(x+3))+(-1*(5*x-15))/((5*x-15)*(x+3)) = 0

(x-4)*(x+3)-1*(5*x-15) = 0

x^2-6*x+3 = 0

x^2-6*x+3 = 0

x^2-6*x+3 = 0

DELTA = (-6)^2-(1*3*4)

DELTA = 24

DELTA > 0

x = (24^(1/2)+6)/(1*2) or x = (6-24^(1/2))/(1*2)

x = (2*6^(1/2)+6)/2 or x = (6-2*6^(1/2))/2

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

((x-((6-2*6^(1/2))/2))*(x-((2*6^(1/2)+6)/2)))/((5*x-15)*(x+3)) = 0

((x-((6-2*6^(1/2))/2))*(x-((2*6^(1/2)+6)/2)))/((5*x-15)*(x+3)) = 0 // * (5*x-15)*(x+3)

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

( x-((2*6^(1/2)+6)/2) )

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

x = (2*6^(1/2)+6)/2

( x-((6-2*6^(1/2))/2) )

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

x = (6-2*6^(1/2))/2

x in { (2*6^(1/2)+6)/2, (6-2*6^(1/2))/2 }

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