1/x+3/(2x)-(x-2)/(4x)=10

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Solution for 1/x+3/(2x)-(x-2)/(4x)=10 equation: 


D( x )

x = 0

4*x = 0

2*x = 0

x = 0

x = 0

4*x = 0

4*x = 0

4*x = 0 // : 4

x = 0

2*x = 0

2*x = 0

2*x = 0 // : 2

x = 0

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

1/x-((x-2)/(4*x))+3/(2*x) = 10 // - 10

1/x-((x-2)/(4*x))+3/(2*x)-10 = 0

(-1*(x-2))/(4*x)+1/x+3/(2*x)-10 = 0

(-1*2*x*x*(x-2))/(2*4*x*x*x)+(1*2*4*x*x)/(2*4*x*x*x)+(3*4*x*x)/(2*4*x*x*x)+(-10*2*4*x*x*x)/(2*4*x*x*x) = 0

1*2*4*x*x-1*2*x*x*(x-2)-10*2*4*x*x*x+3*4*x*x = 0

12*x^2-2*x^3-80*x^3+12*x^2 = 0

24*x^2-2*x^3-80*x^3 = 0

24*x^2-82*x^3 = 0

24*x^2-82*x^3 = 0

2*x^2*(12-41*x) = 0

12-41*x = 0 // - 12

-41*x = -12 // : -41

x = -12/(-41)

x = 12/41

2*x^2*(x-12/41) = 0

(2*x^2*(x-12/41))/(2*4*x*x*x) = 0

(2*x^2*(x-12/41))/(2*4*x*x*x) = 0 // * 2*4*x*x*x

2*x^2*(x-12/41) = 0

( 2*x^2 )

2*x^2 = 0 // : 2

x^2 = 0

x = 0

( x-12/41 )

x-12/41 = 0 // + 12/41

x = 12/41

x in { 0} 

x = 12/41

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