5/(9x+9)=5/(x+1)-(4/9)

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Solution for 5/(9x+9)=5/(x+1)-(4/9) equation: 


D( x )

x+1 = 0

9*x+9 = 0

x+1 = 0

x+1 = 0

x+1 = 0 // - 1

x = -1

9*x+9 = 0

9*x+9 = 0

9*x+9 = 0 // - 9

9*x = -9 // : 9

x = -9/9

x = -1

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

5/(9*x+9) = 5/(x+1)-(4/9) // - 5/(x+1)-(4/9)

5/(9*x+9)-(5/(x+1))+4/9 = 0

5/(9*x+9)-5*(x+1)^-1+4/9 = 0

5/(9*x+9)-5/(x+1)+4/9 = 0

(5*9*(x+1))/(9*(9*x+9)*(x+1))+(-5*9*(9*x+9))/(9*(9*x+9)*(x+1))+(4*(9*x+9)*(x+1))/(9*(9*x+9)*(x+1)) = 0

5*9*(x+1)-5*9*(9*x+9)+4*(9*x+9)*(x+1) = 0

36*x^2-360*x+72*x-360+36 = 0

36*x^2-288*x-324 = 0

36*x^2-288*x-324 = 0

36*(x^2-8*x-9) = 0

x^2-8*x-9 = 0

DELTA = (-8)^2-(-9*1*4)

DELTA = 100

DELTA > 0

x = (100^(1/2)+8)/(1*2) or x = (8-100^(1/2))/(1*2)

x = 9 or x = -1

36*(x+1)*(x-9) = 0

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

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

36*(x+1)*(x-9) = 0

( x+1 )

x+1 = 0 // - 1

x = -1

( x-9 )

x-9 = 0 // + 9

x = 9

x in { -1} 

x = 9

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