-4/x-1=5/(2x-1)

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


D( x )

x = 0

2*x-1 = 0

x = 0

x = 0

2*x-1 = 0

2*x-1 = 0

2*x-1 = 0 // + 1

2*x = 1 // : 2

x = 1/2

x in (-oo:0) U (0:1/2) U (1/2:+oo)

-4/x-1 = 5/(2*x-1) // - 5/(2*x-1)

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

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

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

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

-4*(2*x-1)-1*x*(2*x-1)-5*x = 0

x-2*x^2-13*x+4 = 0

4-2*x^2-12*x = 0

4-2*x^2-12*x = 0

2*(2-x^2-6*x) = 0

2-x^2-6*x = 0

DELTA = (-6)^2-(-1*2*4)

DELTA = 44

DELTA > 0

x = (44^(1/2)+6)/(-1*2) or x = (6-44^(1/2))/(-1*2)

x = (2*11^(1/2)+6)/(-2) or x = (6-2*11^(1/2))/(-2)

2*(x-((2*11^(1/2)+6)/(-2)))*(x-((6-2*11^(1/2))/(-2))) = 0

(2*(x-((2*11^(1/2)+6)/(-2)))*(x-((6-2*11^(1/2))/(-2))))/(x*(2*x-1)) = 0

(2*(x-((2*11^(1/2)+6)/(-2)))*(x-((6-2*11^(1/2))/(-2))))/(x*(2*x-1)) = 0 // * x*(2*x-1)

2*(x-((2*11^(1/2)+6)/(-2)))*(x-((6-2*11^(1/2))/(-2))) = 0

( 2 )

2 = 0

x belongs to the empty set

( x-((2*11^(1/2)+6)/(-2)) )

x-((2*11^(1/2)+6)/(-2)) = 0 // + (2*11^(1/2)+6)/(-2)

x = (2*11^(1/2)+6)/(-2)

( x-((6-2*11^(1/2))/(-2)) )

x-((6-2*11^(1/2))/(-2)) = 0 // + (6-2*11^(1/2))/(-2)

x = (6-2*11^(1/2))/(-2)

x in { (2*11^(1/2)+6)/(-2), (6-2*11^(1/2))/(-2) }

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