(X/(2x+1))-1=(-4/(7(x-2)))

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Solution for (X/(2x+1))-1=(-4/(7(x-2))) equation: 


D( x )

2*x+1 = 0

7*(x-2) = 0

2*x+1 = 0

2*x+1 = 0

2*x+1 = 0 // - 1

2*x = -1 // : 2

x = -1/2

7*(x-2) = 0

7*(x-2) = 0

x-2 = 0 // + 2

x = 2

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

X/(2*x+1)-1 = -4/(7*(x-2)) // + -4/(7*(x-2))

X/(2*x+1)-(-4/(7*(x-2)))-1 = 0

X/(2*x+1)+(4/7)*(x-2)^-1-1 = 0

X/(2*x+1)+4/7/(x-2)-1 = 0

(X*(x-2))/((2*x+1)*(x-2))+(4/7*(2*x+1))/((2*x+1)*(x-2))+(-1*(2*x+1)*(x-2))/((2*x+1)*(x-2)) = 0

X*(x-2)+4/7*(2*x+1)-1*(2*x+1)*(x-2) = 0

X*x-2*X-2*x^2+8/7*x+3*x+4/7+2 = 0

X*x-2*X-2*x^2+29/7*x+18/7 = 0

(X*x-2*X-2*x^2+29/7*x+18/7)/((2*x+1)*(x-2)) = 0

(X*x-2*X-2*x^2+29/7*x+18/7)/((2*x+1)*(x-2)) = 0 // * (2*x+1)*(x-2)

X*x-2*X-2*x^2+29/7*x+18/7 = 0

29/7*x-2*X-2*x^2+18/7 = 0

DELTA = (29/7)^2-(-2*4*(18/7-2*X))

DELTA = 8*(18/7-2*X)+841/49

8*(18/7-2*X)+841/49 = 0

(8*49*(18/7-2*X))/49+841/49 = 0

8*49*(18/7-2*X)+841 = 0

1849-784*X = 0

(1849-784*X)/49 = 0

(1849-784*X)/49 = 0 // * 49

1849-784*X = 0

1849-784*X = 0 // - 1849

-784*X = -1849 // : -784

X = -1849/(-784)

X = 1849/784

DELTA = 0  <=>  t_3 = 1849/784

x = -29/7/(-2*2) i X = 1849/784

x = 29/28 i X = 1849/784

( x = ((8*(18/7-2*X)+841/49)^(1/2)-29/7)/(-2*2) or x = (-(8*(18/7-2*X)+841/49)^(1/2)-29/7)/(-2*2) ) i X > 1849/784

( x = ((8*(18/7-2*X)+841/49)^(1/2)-29/7)/(-4) or x = ((8*(18/7-2*X)+841/49)^(1/2)+29/7)/4 ) i X > 1849/784

X-1849/784 > 0

X-1849/784 > 0 // + 1849/784

X > 1849/784

x in { 29/28, ((8*(18/7-2*X)+841/49)^(1/2)-29/7)/(-4), ((8*(18/7-2*X)+841/49)^(1/2)+29/7)/4 }

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