(3x-5)/x=(2x-3)/x-(x-2)/2

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Solution for (3x-5)/x=(2x-3)/x-(x-2)/2 equation:


D( x )

x = 0

x = 0

x = 0

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

(3*x-5)/x = (2*x-3)/x-((x-2)/2) // - (2*x-3)/x-((x-2)/2)

(3*x-5)/x-((2*x-3)/x)+(x-2)/2 = 0

(3*x-5)/x+(-1*(2*x-3))/x+(x-2)/2 = 0

(2*(3*x-5))/(2*x)+(-1*2*(2*x-3))/(2*x)+(x*(x-2))/(2*x) = 0

2*(3*x-5)-1*2*(2*x-3)+x*(x-2) = 0

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

x^2-4 = 0

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

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

x^2-4 = 0

1*x^2 = 4 // : 1

x^2 = 4

x^2 = 4 // ^ 1/2

abs(x) = 2

x = 2 or x = -2

x in { 2, -2 }

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