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

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Solution for 8/(x+1)-5/2=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)-(5/2) = 4/(3*x+3) // - 4/(3*x+3)

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

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

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

(2*8*(3*x+3))/(2*(x+1)*(3*x+3))+(-4*2*(x+1))/(2*(x+1)*(3*x+3))+(-5*(x+1)*(3*x+3))/(2*(x+1)*(3*x+3)) = 0

2*8*(3*x+3)-4*2*(x+1)-5*(x+1)*(3*x+3) = 0

40*x-15*x^2-30*x-15+40 = 0

10*x-15*x^2+25 = 0

10*x-15*x^2+25 = 0

5*(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

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

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

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

5*(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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