6/(x+1)-(3/2)=6/(3x+3)

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Solution for 6/(x+1)-(3/2)=6/(3x+3) equation: 


D( x )

3*x+3 = 0

x+1 = 0

3*x+3 = 0

3*x+3 = 0

3*x+3 = 0 // - 3

3*x = -3 // : 3

x = -3/3

x = -1

x+1 = 0

x+1 = 0

x+1 = 0 // - 1

x = -1

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

6/(x+1)-(3/2) = 6/(3*x+3) // - 6/(3*x+3)

6/(x+1)-(6/(3*x+3))-(3/2) = 0

6/(x+1)-6*(3*x+3)^-1-3/2 = 0

6/(x+1)-6/(3*x+3)-3/2 = 0

(2*6*(3*x+3))/(2*(x+1)*(3*x+3))+(-6*2*(x+1))/(2*(x+1)*(3*x+3))+(-3*(x+1)*(3*x+3))/(2*(x+1)*(3*x+3)) = 0

2*6*(3*x+3)-6*2*(x+1)-3*(x+1)*(3*x+3) = 0

24*x-9*x^2-18*x-9+24 = 0

6*x-9*x^2+15 = 0

6*x-9*x^2+15 = 0

3*(2*x-3*x^2+5) = 0

2*x-3*x^2+5 = 0

DELTA = 2^2-(-3*4*5)

DELTA = 64

DELTA > 0

x = (64^(1/2)-2)/(-3*2) or x = (-64^(1/2)-2)/(-3*2)

x = -1 or x = 5/3

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

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

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

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

( x+1 )

x+1 = 0 // - 1

x = -1

( x-5/3 )

x-5/3 = 0 // + 5/3

x = 5/3

x in { -1} 

x = 5/3

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