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

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


D( x )

x = 0

x-1 = 0

x = 0

x = 0

x-1 = 0

x-1 = 0

x-1 = 0 // + 1

x = 1

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

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

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

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

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

4*x^2-5*x^2+2*x+5*x-2 = 0

7*x-x^2-2 = 0

7*x-x^2-2 = 0

7*x-x^2-2 = 0

DELTA = 7^2-(-2*(-1)*4)

DELTA = 41

DELTA > 0

x = (41^(1/2)-7)/(-1*2) or x = (-41^(1/2)-7)/(-1*2)

x = (41^(1/2)-7)/(-2) or x = (41^(1/2)+7)/2

(x-((41^(1/2)-7)/(-2)))*(x-((41^(1/2)+7)/2)) = 0

((x-((41^(1/2)-7)/(-2)))*(x-((41^(1/2)+7)/2)))/(x*(x-1)) = 0

((x-((41^(1/2)-7)/(-2)))*(x-((41^(1/2)+7)/2)))/(x*(x-1)) = 0 // * x*(x-1)

(x-((41^(1/2)-7)/(-2)))*(x-((41^(1/2)+7)/2)) = 0

( x-((41^(1/2)+7)/2) )

x-((41^(1/2)+7)/2) = 0 // + (41^(1/2)+7)/2

x = (41^(1/2)+7)/2

( x-((41^(1/2)-7)/(-2)) )

x-((41^(1/2)-7)/(-2)) = 0 // + (41^(1/2)-7)/(-2)

x = (41^(1/2)-7)/(-2)

x in { (41^(1/2)+7)/2, (41^(1/2)-7)/(-2) }

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