(2x+1)/x+x/(2x+1)=58/21

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Solution for (2x+1)/x+x/(2x+1)=58/21 equation:


D( x )

2*x+1 = 0

x = 0

2*x+1 = 0

2*x+1 = 0

2*x+1 = 0 // - 1

2*x = -1 // : 2

x = -1/2

x = 0

x = 0

x in (-oo:-1/2) U (-1/2:0) U (0:+oo)

(2*x+1)/x+x/(2*x+1) = 58/21 // - 58/21

(2*x+1)/x+x/(2*x+1)-(58/21) = 0

(2*x+1)/x+x/(2*x+1)-58/21 = 0

(21*(2*x+1)^2)/(21*x*(2*x+1))+(21*x^2)/(21*x*(2*x+1))+(-58*x*(2*x+1))/(21*x*(2*x+1)) = 0

21*(2*x+1)^2-58*x*(2*x+1)+21*x^2 = 0

105*x^2-116*x^2+84*x-58*x+21 = 0

26*x-11*x^2+21 = 0

26*x-11*x^2+21 = 0

26*x-11*x^2+21 = 0

DELTA = 26^2-(-11*4*21)

DELTA = 1600

DELTA > 0

x = (1600^(1/2)-26)/(-11*2) or x = (-1600^(1/2)-26)/(-11*2)

x = -7/11 or x = 3

(x+7/11)*(x-3) = 0

((x+7/11)*(x-3))/(21*x*(2*x+1)) = 0

((x+7/11)*(x-3))/(21*x*(2*x+1)) = 0 // * 21*x*(2*x+1)

(x+7/11)*(x-3) = 0

( x+7/11 )

x+7/11 = 0 // - 7/11

x = -7/11

( x-3 )

x-3 = 0 // + 3

x = 3

x in { -7/11, 3 }

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