(x/4-(x^2-8x)/(4x-5))=1/(12x-12)

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Solution for (x/4-(x^2-8x)/(4x-5))=1/(12x-12) equation:


D( x )

12*x-12 = 0

4*x-5 = 0

12*x-12 = 0

12*x-12 = 0

12*x-12 = 0 // + 12

12*x = 12 // : 12

x = 12/12

x = 1

4*x-5 = 0

4*x-5 = 0

4*x-5 = 0 // + 5

4*x = 5 // : 4

x = 5/4

x in (-oo:1) U (1:5/4) U (5/4:+oo)

x/4-((x^2-(8*x))/(4*x-5)) = 1/(12*x-12) // - 1/(12*x-12)

x/4-((x^2-(8*x))/(4*x-5))-(1/(12*x-12)) = 0

x/4-((x^2-8*x)/(4*x-5))-(12*x-12)^-1 = 0

(-1*(x^2-8*x))/(4*x-5)-1/(12*x-12)+x/4 = 0

(-1*4*(x^2-8*x)*(12*x-12))/(4*(4*x-5)*(12*x-12))+(-1*4*(4*x-5))/(4*(4*x-5)*(12*x-12))+(x*(4*x-5)*(12*x-12))/(4*(4*x-5)*(12*x-12)) = 0

x*(4*x-5)*(12*x-12)-1*4*(x^2-8*x)*(12*x-12)-1*4*(4*x-5) = 0

48*x^3-48*x^3+432*x^2-108*x^2-400*x+60*x+20 = 0

324*x^2-340*x+20 = 0

324*x^2-340*x+20 = 0

4*(81*x^2-85*x+5) = 0

81*x^2-85*x+5 = 0

DELTA = (-85)^2-(4*5*81)

DELTA = 5605

DELTA > 0

x = (5605^(1/2)+85)/(2*81) or x = (85-5605^(1/2))/(2*81)

x = (5605^(1/2)+85)/162 or x = (85-5605^(1/2))/162

4*(x-((85-5605^(1/2))/162))*(x-((5605^(1/2)+85)/162)) = 0

(4*(x-((85-5605^(1/2))/162))*(x-((5605^(1/2)+85)/162)))/(4*(4*x-5)*(12*x-12)) = 0

(4*(x-((85-5605^(1/2))/162))*(x-((5605^(1/2)+85)/162)))/(4*(4*x-5)*(12*x-12)) = 0 // * 4*(4*x-5)*(12*x-12)

4*(x-((85-5605^(1/2))/162))*(x-((5605^(1/2)+85)/162)) = 0

( x-((5605^(1/2)+85)/162) )

x-((5605^(1/2)+85)/162) = 0 // + (5605^(1/2)+85)/162

x = (5605^(1/2)+85)/162

( x-((85-5605^(1/2))/162) )

x-((85-5605^(1/2))/162) = 0 // + (85-5605^(1/2))/162

x = (85-5605^(1/2))/162

x in { (5605^(1/2)+85)/162, (85-5605^(1/2))/162 }

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