(x-3)/(5x-24)=1/(x-4)

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Solution for (x-3)/(5x-24)=1/(x-4) equation:


D( x )

5*x-24 = 0

x-4 = 0

5*x-24 = 0

5*x-24 = 0

5*x-24 = 0 // + 24

5*x = 24 // : 5

x = 24/5

x-4 = 0

x-4 = 0

x-4 = 0 // + 4

x = 4

x in (-oo:4) U (4:24/5) U (24/5:+oo)

(x-3)/(5*x-24) = 1/(x-4) // - 1/(x-4)

(x-3)/(5*x-24)-(1/(x-4)) = 0

(x-3)/(5*x-24)-(x-4)^-1 = 0

(x-3)/(5*x-24)-1/(x-4) = 0

((x-3)*(x-4))/((5*x-24)*(x-4))+(-1*(5*x-24))/((5*x-24)*(x-4)) = 0

(x-3)*(x-4)-1*(5*x-24) = 0

x^2-12*x+36 = 0

x^2-12*x+36 = 0

x^2-12*x+36 = 0

DELTA = (-12)^2-(1*4*36)

DELTA = 0

x = 12/(1*2)

x = 6 or x = 6

(x-6)^2 = 0

((x-6)^2)/((5*x-24)*(x-4)) = 0

((x-6)^2)/((5*x-24)*(x-4)) = 0 // * (5*x-24)*(x-4)

(x-6)^2 = 0

x-6 = 0 // + 6

x = 6

x in { 6, 6 }

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