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

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


D( x )

x = 0

x+3 = 0

x = 0

x = 0

x+3 = 0

x+3 = 0

x+3 = 0 // - 3

x = -3

x in (-oo:-3) U (-3:0) U (0:+oo)

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

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

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

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

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

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

x^2-2*x-6 = 0

x^2-2*x-6 = 0

x^2-2*x-6 = 0

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

DELTA = 28

DELTA > 0

x = (28^(1/2)+2)/(1*2) or x = (2-28^(1/2))/(1*2)

x = (2*7^(1/2)+2)/2 or x = (2-2*7^(1/2))/2

(x-((2-2*7^(1/2))/2))*(x-((2*7^(1/2)+2)/2)) = 0

((x-((2-2*7^(1/2))/2))*(x-((2*7^(1/2)+2)/2)))/(x*(x+3)) = 0

((x-((2-2*7^(1/2))/2))*(x-((2*7^(1/2)+2)/2)))/(x*(x+3)) = 0 // * x*(x+3)

(x-((2-2*7^(1/2))/2))*(x-((2*7^(1/2)+2)/2)) = 0

( x-((2*7^(1/2)+2)/2) )

x-((2*7^(1/2)+2)/2) = 0 // + (2*7^(1/2)+2)/2

x = (2*7^(1/2)+2)/2

( x-((2-2*7^(1/2))/2) )

x-((2-2*7^(1/2))/2) = 0 // + (2-2*7^(1/2))/2

x = (2-2*7^(1/2))/2

x in { (2*7^(1/2)+2)/2, (2-2*7^(1/2))/2 }

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