(x/(x+2))-(2/(2x-1))=(1/5)

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Solution for (x/(x+2))-(2/(2x-1))=(1/5) 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)

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

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

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

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

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

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

10*x^2-2*x^2-15*x-3*x-20+2 = 0

8*x^2-18*x-18 = 0

8*x^2-18*x-18 = 0

2*(4*x^2-9*x-9) = 0

4*x^2-9*x-9 = 0

DELTA = (-9)^2-(-9*4*4)

DELTA = 225

DELTA > 0

x = (225^(1/2)+9)/(2*4) or x = (9-225^(1/2))/(2*4)

x = 3 or x = -3/4

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

(2*(x+3/4)*(x-3))/(5*(x+2)*(2*x-1)) = 0

(2*(x+3/4)*(x-3))/(5*(x+2)*(2*x-1)) = 0 // * 5*(x+2)*(2*x-1)

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

( x+3/4 )

x+3/4 = 0 // - 3/4

x = -3/4

( x-3 )

x-3 = 0 // + 3

x = 3

x in { -3/4, 3 }

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