(8x^-2-2x^-1)/(10x^-1-12x^-2)

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Solution for (8x^-2-2x^-1)/(10x^-1-12x^-2) equation:


D( x )

x = 0

10*x^-1-(12*x^-2) = 0

x = 0

x = 0

10*x^-1-(12*x^-2) = 0

10*x^-1-(12*x^-2) = 0

10*x^-1-12*x^-2 = 0

t_1 = x^-1

10*t_1^1-12*t_1^2 = 0

10*t_1-12*t_1^2 = 0

DELTA = 10^2-(-12*0*4)

DELTA = 100

DELTA > 0

t_1 = (100^(1/2)-10)/(-12*2) or t_1 = (-100^(1/2)-10)/(-12*2)

t_1 = 0 or t_1 = 5/6

t_1 = 0

x^-1+0 = 0

x^-1 = 0

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

x^-1 = 0

x należy do O

t_1 = 5/6

x^-1-5/6 = 0

1*x^-1 = 5/6 // : 1

x^-1 = 5/6

-1 < 0

1/(x^1) = 5/6 // * x^1

1 = 5/6*x^1 // : 5/6

6/5 = x^1

x = 6/5

x in (-oo:0) U (0:6/5) U (6/5:+oo)

(8*x^-2-(2*x^-1))/(10*x^-1-(12*x^-2)) = 0

(8*x^-2-2*x^-1)/(10*x^-1-12*x^-2) = 0

8*x^-2-2*x^-1 = 0

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

4*x^-1 = 1 // : 4

x^-1 = 1/4

-1 < 0

1/(x^1) = 1/4 // * x^1

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

4 = x^1

x = 4

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

10*x^-1-12*x^-2 = 0

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

-6*x^-1 = -5 // : -6

x^-1 = 5/6

-1 < 0

1/(x^1) = 5/6 // * x^1

1 = 5/6*x^1 // : 5/6

6/5 = x^1

x = 6/5

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

(2*x^-1*(x-4))/(2*x^-1*(x-6/5)) = 0

( 2*x^-1 )

2*x^-1 = 0 // : 2

x^-1 = 0

x należy do O

( x-4 )

x-4 = 0 // + 4

x = 4

x = 4

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