(x-5)/(3x-15)=2/x

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Solution for (x-5)/(3x-15)=2/x equation:


D( x )

x = 0

3*x-15 = 0

x = 0

x = 0

3*x-15 = 0

3*x-15 = 0

3*x-15 = 0 // + 15

3*x = 15 // : 3

x = 15/3

x = 5

x in (-oo:0) U (0:5) U (5:+oo)

(x-5)/(3*x-15) = 2/x // - 2/x

(x-5)/(3*x-15)-(2/x) = 0

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

(x-5)/(3*x-15)-2/x = 0

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

x*(x-5)-2*(3*x-15) = 0

x^2-11*x+30 = 0

x^2-11*x+30 = 0

x^2-11*x+30 = 0

DELTA = (-11)^2-(1*4*30)

DELTA = 1

DELTA > 0

x = (1^(1/2)+11)/(1*2) or x = (11-1^(1/2))/(1*2)

x = 6 or x = 5

(x-5)*(x-6) = 0

((x-5)*(x-6))/(x*(3*x-15)) = 0

((x-5)*(x-6))/(x*(3*x-15)) = 0 // * x*(3*x-15)

(x-5)*(x-6) = 0

( x-5 )

x-5 = 0 // + 5

x = 5

( x-6 )

x-6 = 0 // + 6

x = 6

x in { 5}

x = 6

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