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

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


D( x )

x+2 = 0

2*x-1 = 0

x+2 = 0

x+2 = 0

x+2 = 0 // - 2

x = -2

2*x-1 = 0

2*x-1 = 0

2*x-1 = 0 // + 1

2*x = 1 // : 2

x = 1/2

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

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

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

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

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

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

15*x^2-20*x^2-30*x+15+20 = 0

35-5*x^2-30*x = 0

35-5*x^2-30*x = 0

5*(7-x^2-6*x) = 0

7-x^2-6*x = 0

DELTA = (-6)^2-(-1*4*7)

DELTA = 64

DELTA > 0

x = (64^(1/2)+6)/(-1*2) or x = (6-64^(1/2))/(-1*2)

x = -7 or x = 1

5*(x+7)*(x-1) = 0

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

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

5*(x+7)*(x-1) = 0

( x+7 )

x+7 = 0 // - 7

x = -7

( x-1 )

x-1 = 0 // + 1

x = 1

x in { -7, 1 }

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