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

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


D( x )

x = 0

x = 0

x = 0

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

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

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

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

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

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

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

2*x^2+8*x-6*x-3 = 0

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

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

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

DELTA = 2^2-(-3*2*4)

DELTA = 28

DELTA > 0

x = (28^(1/2)-2)/(2*2) or x = (-28^(1/2)-2)/(2*2)

x = (2*7^(1/2)-2)/4 or x = (-2*7^(1/2)-2)/4

(x-((-2*7^(1/2)-2)/4))*(x-((2*7^(1/2)-2)/4)) = 0

((x-((-2*7^(1/2)-2)/4))*(x-((2*7^(1/2)-2)/4)))/(3*x) = 0

((x-((-2*7^(1/2)-2)/4))*(x-((2*7^(1/2)-2)/4)))/(3*x) = 0 // * 3*x

(x-((-2*7^(1/2)-2)/4))*(x-((2*7^(1/2)-2)/4)) = 0

( x-((-2*7^(1/2)-2)/4) )

x-((-2*7^(1/2)-2)/4) = 0 // + (-2*7^(1/2)-2)/4

x = (-2*7^(1/2)-2)/4

( x-((2*7^(1/2)-2)/4) )

x-((2*7^(1/2)-2)/4) = 0 // + (2*7^(1/2)-2)/4

x = (2*7^(1/2)-2)/4

x in { (-2*7^(1/2)-2)/4, (2*7^(1/2)-2)/4 }

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