(5x+4/4x+3)/(x-10/x-8)

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Solution for (5x+4/4x+3)/(x-10/x-8) equation: 


D( x )

x = 0

x-(10/x)-8 = 0

x = 0

x = 0

x-(10/x)-8 = 0

x-(10/x)-8 = 0

x-10*x^-1-8 = 0

1*x^1-10*x^-1-8*x^0 = 0

(1*x^2-8*x^1-10*x^0)/(x^1) = 0 // * x^2

x^1*(1*x^2-8*x^1-10*x^0) = 0

x^1

x^2-8*x-10 = 0

x^2-8*x-10 = 0

DELTA = (-8)^2-(-10*1*4)

DELTA = 104

DELTA > 0

x = (104^(1/2)+8)/(1*2) or x = (8-104^(1/2))/(1*2)

x = (2*26^(1/2)+8)/2 or x = (8-2*26^(1/2))/2

x in { (8-2*26^(1/2))/2, (2*26^(1/2)+8)/2} 

x in (-oo:(8-2*26^(1/2))/2) U ((8-2*26^(1/2))/2:0) U (0:(2*26^(1/2)+8)/2) U ((2*26^(1/2)+8)/2:+oo)

(5*x+(4/4)*x+3)/(x-(10/x)-8) = 0

(5*x+(4/4)*x+3)/(x-10*x^-1-8) = 0

(6*x+3)/(x-10*x^-1-8) = 0

x-10*x^-1-8 = 0

1*x^1-10*x^-1-8*x^0 = 0

(1*x^2-8*x^1-10*x^0)/(x^1) = 0 // * x^2

x^1*(1*x^2-8*x^1-10*x^0) = 0

x^1

x^2-8*x-10 = 0

x^2-8*x-10 = 0

DELTA = (-8)^2-(-10*1*4)

DELTA = 104

DELTA > 0

x = (104^(1/2)+8)/(1*2) or x = (8-104^(1/2))/(1*2)

x = (2*26^(1/2)+8)/2 or x = (8-2*26^(1/2))/2

x in { (8-2*26^(1/2))/2, (2*26^(1/2)+8)/2} 

(x-((8-2*26^(1/2))/2))*(x-((2*26^(1/2)+8)/2)) = 0

(6*x+3)/((x-((8-2*26^(1/2))/2))*(x-((2*26^(1/2)+8)/2))) = 0

6*x+3 = 0 // - 3

6*x = -3 // : 6

x = -3/6

x = -1/2

x = -1/2

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