(1/x)(1/(x+9))=(17/(9x+21))

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Solution for (1/x)(1/(x+9))=(17/(9x+21)) equation: 


D( x )

9*x+21 = 0

x = 0

x+9 = 0

9*x+21 = 0

9*x+21 = 0

9*x+21 = 0 // - 21

9*x = -21 // : 9

x = -21/9

x = -7/3

x = 0

x = 0

x+9 = 0

x+9 = 0

x+9 = 0 // - 9

x = -9

x in (-oo:-9) U (-9:-7/3) U (-7/3:0) U (0:+oo)

(1/x)*(1/(x+9)) = 17/(9*x+21) // - 17/(9*x+21)

(1/x)*(1/(x+9))-(17/(9*x+21)) = 0

(1/x)*(1/(x+9))-17*(9*x+21)^-1 = 0

(1*x^-1)/(x+9)-17/(9*x+21) = 0

(1*x^-1*(9*x+21))/((x+9)*(9*x+21))+(-17*(x+9))/((x+9)*(9*x+21)) = 0

1*x^-1*(9*x+21)-17*(x+9) = 0

21*x^-1-17*x-144 = 0

21*x^-1-17*x-144 = 0

21*x^-1-17*x^1-144*x^0 = 0

(21*x^0-17*x^2-144*x^1)/(x^1) = 0 // * x^2

x^1*(21*x^0-17*x^2-144*x^1) = 0

x^1

21-17*x^2-144*x = 0

21-17*x^2-144*x = 0

DELTA = (-144)^2-(-17*4*21)

DELTA = 22164

DELTA > 0

x = (22164^(1/2)+144)/(-17*2) or x = (144-22164^(1/2))/(-17*2)

x = (2*5541^(1/2)+144)/(-34) or x = (144-2*5541^(1/2))/(-34)

x in { (2*5541^(1/2)+144)/(-34), (144-2*5541^(1/2))/(-34)} 

(x-((2*5541^(1/2)+144)/(-34)))*(x-((144-2*5541^(1/2))/(-34))) = 0

((x-((2*5541^(1/2)+144)/(-34)))*(x-((144-2*5541^(1/2))/(-34))))/((x+9)*(9*x+21)) = 0

((x-((2*5541^(1/2)+144)/(-34)))*(x-((144-2*5541^(1/2))/(-34))))/((x+9)*(9*x+21)) = 0 // * (x+9)*(9*x+21)

(x-((2*5541^(1/2)+144)/(-34)))*(x-((144-2*5541^(1/2))/(-34))) = 0

( x-((144-2*5541^(1/2))/(-34)) )

x-((144-2*5541^(1/2))/(-34)) = 0 // + (144-2*5541^(1/2))/(-34)

x = (144-2*5541^(1/2))/(-34)

( x-((2*5541^(1/2)+144)/(-34)) )

x-((2*5541^(1/2)+144)/(-34)) = 0 // + (2*5541^(1/2)+144)/(-34)

x = (2*5541^(1/2)+144)/(-34)

x in { (144-2*5541^(1/2))/(-34), (2*5541^(1/2)+144)/(-34) }

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