(2x+3)/(2x+1)=(8)/(2x+3)

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Solution for (2x+3)/(2x+1)=(8)/(2x+3) equation: 


D( x )

2*x+1 = 0

2*x+3 = 0

2*x+1 = 0

2*x+1 = 0

2*x+1 = 0 // - 1

2*x = -1 // : 2

x = -1/2

2*x+3 = 0

2*x+3 = 0

2*x+3 = 0 // - 3

2*x = -3 // : 2

x = -3/2

x in (-oo:-3/2) U (-3/2:-1/2) U (-1/2:+oo)

(2*x+3)/(2*x+1) = 8/(2*x+3) // - 8/(2*x+3)

(2*x+3)/(2*x+1)-(8/(2*x+3)) = 0

(2*x+3)/(2*x+1)-8*(2*x+3)^-1 = 0

(2*x+3)/(2*x+1)-8/(2*x+3) = 0

((2*x+3)^2)/((2*x+1)*(2*x+3))+(-8*(2*x+1))/((2*x+1)*(2*x+3)) = 0

(2*x+3)^2-8*(2*x+1) = 0

4*x^2-4*x+1 = 0

4*x^2-4*x+1 = 0

4*x^2-4*x+1 = 0

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

DELTA = 0

x = 4/(2*4)

x = 1/2 or x = 1/2

(x-1/2)^2 = 0

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

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

(x-1/2)^2 = 0

x-1/2 = 0 // + 1/2

x = 1/2

x in { 1/2, 1/2 }

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