(4/(9x+9))=(6/(x+1))-(5/9)

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Solution for (4/(9x+9))=(6/(x+1))-(5/9) 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)

4/(9*x+9) = 6/(x+1)-(5/9) // - 6/(x+1)-(5/9)

4/(9*x+9)-(6/(x+1))+5/9 = 0

4/(9*x+9)-6*(x+1)^-1+5/9 = 0

4/(9*x+9)-6/(x+1)+5/9 = 0

(4*9*(x+1))/(9*(9*x+9)*(x+1))+(-6*9*(9*x+9))/(9*(9*x+9)*(x+1))+(5*(9*x+9)*(x+1))/(9*(9*x+9)*(x+1)) = 0

4*9*(x+1)-6*9*(9*x+9)+5*(9*x+9)*(x+1) = 0

45*x^2-450*x+90*x-450+45 = 0

45*x^2-360*x-405 = 0

45*x^2-360*x-405 = 0

45*(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

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

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

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

45*(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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