(21/x)-(21/(x-4))=-4

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Solution for (21/x)-(21/(x-4))=-4 equation: 


D( x )

x = 0

x-4 = 0

x = 0

x = 0

x-4 = 0

x-4 = 0

x-4 = 0 // + 4

x = 4

x in (-oo:0) U (0:4) U (4:+oo)

21/x-(21/(x-4)) = -4 // + 4

21/x-(21/(x-4))+4 = 0

21/x-21*(x-4)^-1+4 = 0

21/x-21/(x-4)+4 = 0

(-21*x)/(x*(x-4))+(21*(x-4))/(x*(x-4))+(4*x*(x-4))/(x*(x-4)) = 0

21*(x-4)+4*x*(x-4)-21*x = 0

4*x^2-16*x-84 = 0

4*x^2-16*x-84 = 0

4*(x^2-4*x-21) = 0

x^2-4*x-21 = 0

DELTA = (-4)^2-(-21*1*4)

DELTA = 100

DELTA > 0

x = (100^(1/2)+4)/(1*2) or x = (4-100^(1/2))/(1*2)

x = 7 or x = -3

4*(x+3)*(x-7) = 0

(4*(x+3)*(x-7))/(x*(x-4)) = 0

(4*(x+3)*(x-7))/(x*(x-4)) = 0 // * x*(x-4)

4*(x+3)*(x-7) = 0

( 4 )

4 = 0

x belongs to the empty set

( x+3 )

x+3 = 0 // - 3

x = -3

( x-7 )

x-7 = 0 // + 7

x = 7

x in { -3, 7 }

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