(1/x)+(1/x-7)=15/(7x-21)

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Solution for (1/x)+(1/x-7)=15/(7x-21) equation: 


D( x )

x = 0

7*x-21 = 0

x = 0

x = 0

7*x-21 = 0

7*x-21 = 0

7*x-21 = 0 // + 21

7*x = 21 // : 7

x = 21/7

x = 3

x in (-oo:0) U (0:3) U (3:+oo)

1/x+1/x-7 = 15/(7*x-21) // - 15/(7*x-21)

1/x-(15/(7*x-21))+1/x-7 = 0

1/x-15*(7*x-21)^-1+1/x-7 = 0

1/x-15/(7*x-21)+1/x-7 = 0

(-15*x)/(x*(7*x-21))+(1*(7*x-21))/(x*(7*x-21))+(1*(7*x-21))/(x*(7*x-21))+(-7*x*(7*x-21))/(x*(7*x-21)) = 0

1*(7*x-21)+1*(7*x-21)-7*x*(7*x-21)-15*x = 0

7*x-49*x^2-8*x+147*x-21-21 = 0

147*x-49*x^2-x-42 = 0

146*x-49*x^2-42 = 0

146*x-49*x^2-42 = 0

146*x-49*x^2-42 = 0

DELTA = 146^2-(-49*(-42)*4)

DELTA = 13084

DELTA > 0

x = (13084^(1/2)-146)/(-49*2) or x = (-13084^(1/2)-146)/(-49*2)

x = (2*3271^(1/2)-146)/(-98) or x = (-2*3271^(1/2)-146)/(-98)

(x-((2*3271^(1/2)-146)/(-98)))*(x-((-2*3271^(1/2)-146)/(-98))) = 0

((x-((2*3271^(1/2)-146)/(-98)))*(x-((-2*3271^(1/2)-146)/(-98))))/(x*(7*x-21)) = 0

((x-((2*3271^(1/2)-146)/(-98)))*(x-((-2*3271^(1/2)-146)/(-98))))/(x*(7*x-21)) = 0 // * x*(7*x-21)

(x-((2*3271^(1/2)-146)/(-98)))*(x-((-2*3271^(1/2)-146)/(-98))) = 0

( x-((-2*3271^(1/2)-146)/(-98)) )

x-((-2*3271^(1/2)-146)/(-98)) = 0 // + (-2*3271^(1/2)-146)/(-98)

x = (-2*3271^(1/2)-146)/(-98)

( x-((2*3271^(1/2)-146)/(-98)) )

x-((2*3271^(1/2)-146)/(-98)) = 0 // + (2*3271^(1/2)-146)/(-98)

x = (2*3271^(1/2)-146)/(-98)

x in { (-2*3271^(1/2)-146)/(-98), (2*3271^(1/2)-146)/(-98) }

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