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

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Solution for (3-x)/(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)

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

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

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

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

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

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

2*x-x^2+12 = 0

2*x-x^2+12 = 0

2*x-x^2+12 = 0

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

DELTA = 52

DELTA > 0

x = (52^(1/2)-2)/(-1*2) or x = (-52^(1/2)-2)/(-1*2)

x = (2*13^(1/2)-2)/(-2) or x = (-2*13^(1/2)-2)/(-2)

(x-((2*13^(1/2)-2)/(-2)))*(x-((-2*13^(1/2)-2)/(-2))) = 0

((x-((2*13^(1/2)-2)/(-2)))*(x-((-2*13^(1/2)-2)/(-2))))/((5*x-24)*(x-4)) = 0

((x-((2*13^(1/2)-2)/(-2)))*(x-((-2*13^(1/2)-2)/(-2))))/((5*x-24)*(x-4)) = 0 // * (5*x-24)*(x-4)

(x-((2*13^(1/2)-2)/(-2)))*(x-((-2*13^(1/2)-2)/(-2))) = 0

( x-((-2*13^(1/2)-2)/(-2)) )

x-((-2*13^(1/2)-2)/(-2)) = 0 // + (-2*13^(1/2)-2)/(-2)

x = (-2*13^(1/2)-2)/(-2)

( x-((2*13^(1/2)-2)/(-2)) )

x-((2*13^(1/2)-2)/(-2)) = 0 // + (2*13^(1/2)-2)/(-2)

x = (2*13^(1/2)-2)/(-2)

x in { (-2*13^(1/2)-2)/(-2), (2*13^(1/2)-2)/(-2) }

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