(8/(x+1))-(3/2)=(4/(3x+3))

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Solution for (8/(x+1))-(3/2)=(4/(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)

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

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

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

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

(2*8*(3*x+3))/(2*(x+1)*(3*x+3))+(-4*2*(x+1))/(2*(x+1)*(3*x+3))+(-3*(x+1)*(3*x+3))/(2*(x+1)*(3*x+3)) = 0

2*8*(3*x+3)-4*2*(x+1)-3*(x+1)*(3*x+3) = 0

40*x-9*x^2-18*x-9+40 = 0

22*x-9*x^2+31 = 0

22*x-9*x^2+31 = 0

22*x-9*x^2+31 = 0

DELTA = 22^2-(-9*4*31)

DELTA = 1600

DELTA > 0

x = (1600^(1/2)-22)/(-9*2) or x = (-1600^(1/2)-22)/(-9*2)

x = -1 or x = 31/9

(x+1)*(x-31/9) = 0

((x+1)*(x-31/9))/(2*(x+1)*(3*x+3)) = 0

((x+1)*(x-31/9))/(2*(x+1)*(3*x+3)) = 0 // * 2*(x+1)*(3*x+3)

(x+1)*(x-31/9) = 0

( x+1 )

x+1 = 0 // - 1

x = -1

( x-31/9 )

x-31/9 = 0 // + 31/9

x = 31/9

x in { -1} 

x = 31/9

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