(7x+8)/6x=(5/6+1/x)

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Solution for (7x+8)/6x=(5/6+1/x) equation: 


D( x )

x = 0

x = 0

x = 0

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

x*((7*x+8)/6) = 1/x+5/6 // - 1/x+5/6

x*((7*x+8)/6)-(1/x)-(5/6) = 0

x*((7*x+8)/6)-x^-1-5/6 = 0

(x*(7*x+8))/6-1/x-5/6 = 0

(x^2*(7*x+8))/(6*x)+(-1*6)/(6*x)+(-5*x)/(6*x) = 0

x^2*(7*x+8)-5*x-1*6 = 0

7*x^3+8*x^2-5*x-6 = 0

7*x^3+8*x^2-5*x-6 = 0

7*x^3+8*x^2-5*x-6 = 0

{ 1, -1, 2, -2, 3, -3, 6, -6 }

1

x = 1

7*x^3+8*x^2-5*x-6 = 4

1

-1

x = -1

7*x^3+8*x^2-5*x-6 = 0

-1

x+1

7*x^2+x-6

7*x^3+8*x^2-5*x-6

x+1

-7*x^3-7*x^2

x^2-5*x-6

-x^2-x

-6*x-6

6*x+6

0

7*x^2+x-6 = 0

DELTA = 1^2-(-6*4*7)

DELTA = 169

DELTA > 0

x = (169^(1/2)-1)/(2*7) or x = (-169^(1/2)-1)/(2*7)

x = 6/7 or x = -1

x in { -1, 6/7, -1} 

(x+1)^2*(x-6/7) = 0

((x+1)^2*(x-6/7))/(6*x) = 0

((x+1)^2*(x-6/7))/(6*x) = 0 // * 6*x

(x+1)^2*(x-6/7) = 0

( x+1 )

x+1 = 0 // - 1

x = -1

( x-6/7 )

x-6/7 = 0 // + 6/7

x = 6/7

x in { -1, -1, 6/7 }

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