1/(x+3)-1/(2x+3)=1/18

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Solution for 1/(x+3)-1/(2x+3)=1/18 equation: 


D( x )

x+3 = 0

2*x+3 = 0

x+3 = 0

x+3 = 0

x+3 = 0 // - 3

x = -3

2*x+3 = 0

2*x+3 = 0

2*x+3 = 0 // - 3

2*x = -3 // : 2

x = -3/2

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

1/(x+3)-(1/(2*x+3)) = 1/18 // - 1/18

1/(x+3)-(1/(2*x+3))-(1/18) = 0

1/(x+3)-(2*x+3)^-1-1/18 = 0

1/(x+3)-1/(2*x+3)-1/18 = 0

(1*18*(2*x+3))/(18*(x+3)*(2*x+3))+(-1*18*(x+3))/(18*(x+3)*(2*x+3))+(-1*(x+3)*(2*x+3))/(18*(x+3)*(2*x+3)) = 0

1*18*(2*x+3)-1*18*(x+3)-1*(x+3)*(2*x+3) = 0

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

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

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

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

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

DELTA = 9

DELTA > 0

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

x = 3/2 or x = 3

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

((x-3/2)*(x-3))/(18*(x+3)*(2*x+3)) = 0

((x-3/2)*(x-3))/(18*(x+3)*(2*x+3)) = 0 // * 18*(x+3)*(2*x+3)

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

( x-3/2 )

x-3/2 = 0 // + 3/2

x = 3/2

( x-3 )

x-3 = 0 // + 3

x = 3

x in { 3/2, 3 }

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