((5/x)-(3/4x))/((4/7x)-(1/x))

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Solution for ((5/x)-(3/4x))/((4/7x)-(1/x)) equation: 


D( x )

(4/7)*x-(1/x) = 0

x = 0

(4/7)*x-(1/x) = 0

(4/7)*x-(1/x) = 0

(4/7)*x-x^-1 = 0

4/7*x^1-1*x^-1 = 0

(4/7*x^2-1*x^0)/(x^1) = 0 // * x^2

x^1*(4/7*x^2-1*x^0) = 0

x^1

(4/7)*x^2-1 = 0

(4/7)*x^2-1 = 0

DELTA = 0^2-(-1*4*(4/7))

DELTA = 16/7

DELTA > 0

x = ((16/7)^(1/2)+0)/(2*(4/7)) or x = (0-(16/7)^(1/2))/(2*(4/7))

x = 7/8*(16/7)^(1/2) or x = 7/8*(16/7)^(1/2)

x in { 7/8*(16/7)^(1/2), 7/8*(16/7)^(1/2)} 

x = 0

x = 0

x in (-oo:0) U (0:7/8*(16/7)^(1/2)) U (7/8*(16/7)^(1/2):+oo)

(5/x-((3/4)*x))/((4/7)*x-(1/x)) = 0

((-3/4)*x+5/x)/((4/7)*x-x^-1) = 0

(5*x^-1-3/4*x)/(4/7*x-x^-1) = 0

5*x^-1-3/4*x = 0

x^-1*(5-3/4*x^2) = 0

-3/4*x^2 = -5 // : -3/4

x^2 = 20/3

x^2 = 20/3 // ^ 1/2

abs(x) = (20/3)^(1/2)

x = (20/3)^(1/2) or x = -(20/3)^(1/2)

x^-1*(x-(20/3)^(1/2))*(x+(20/3)^(1/2)) = 0

4/7*x-x^-1 = 0

x^-1*(4/7*x^2-1) = 0

4/7*x^2 = 1 // : 4/7

x^2 = 7/4

x^2 = 7/4 // ^ 1/2

abs(x) = (7/4)^(1/2)

x = (7/4)^(1/2) or x = -(7/4)^(1/2)

x^-1*(x-(7/4)^(1/2))*(x+(7/4)^(1/2)) = 0

(x^-1*(x-(20/3)^(1/2))*(x+(20/3)^(1/2)))/(x^-1*(x-(7/4)^(1/2))*(x+(7/4)^(1/2))) = 0

( x+(20/3)^(1/2) )

x+(20/3)^(1/2) = 0 // - (20/3)^(1/2)

x = -(20/3)^(1/2)

( x-(20/3)^(1/2) )

x-(20/3)^(1/2) = 0 // + (20/3)^(1/2)

x = (20/3)^(1/2)

( x^-1 )

1*x^-1 = 0 // : 1

x^-1 = 0

x należy do O

x in { -(20/3)^(1/2), (20/3)^(1/2) }

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