(2x-9)/(x-1)+(x/2)=5/(x-7)

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Solution for (2x-9)/(x-1)+(x/2)=5/(x-7) equation: 


D( x )

x-7 = 0

x-1 = 0

x-7 = 0

x-7 = 0

x-7 = 0 // + 7

x = 7

x-1 = 0

x-1 = 0

x-1 = 0 // + 1

x = 1

x in (-oo:1) U (1:7) U (7:+oo)

(2*x-9)/(x-1)+x/2 = 5/(x-7) // - 5/(x-7)

(2*x-9)/(x-1)-(5/(x-7))+x/2 = 0

(2*x-9)/(x-1)-5*(x-7)^-1+x/2 = 0

(2*x-9)/(x-1)-5/(x-7)+x/2 = 0

(2*(2*x-9)*(x-7))/(2*(x-1)*(x-7))+(-5*2*(x-1))/(2*(x-1)*(x-7))+(x*(x-1)*(x-7))/(2*(x-1)*(x-7)) = 0

2*(2*x-9)*(x-7)-5*2*(x-1)+x*(x-1)*(x-7) = 0

x^3+4*x^2-8*x^2-56*x+7*x+136 = 0

x^3-4*x^2-49*x+136 = 0

x^3-4*x^2-49*x+136 = 0

x^3-4*x^2-49*x+136 = 0

{ 1, -1, 2, -2, 4, -4, 8, -8, 17, -17, 34, -34, 68, -68, 136, -136 }

1

x = 1

x^3-4*x^2-49*x+136 = 84

1

-1

x = -1

x^3-4*x^2-49*x+136 = 180

-1

2

x = 2

x^3-4*x^2-49*x+136 = 30

2

-2

x = -2

x^3-4*x^2-49*x+136 = 210

-2

4

x = 4

x^3-4*x^2-49*x+136 = -60

4

-4

x = -4

x^3-4*x^2-49*x+136 = 204

-4

8

x = 8

x^3-4*x^2-49*x+136 = 0

8

x-8

x^2+4*x-17

x^3-4*x^2-49*x+136

x-8

8*x^2-x^3

4*x^2-49*x+136

32*x-4*x^2

136-17*x

17*x-136

0

x^2+4*x-17 = 0

DELTA = 4^2-(-17*1*4)

DELTA = 84

DELTA > 0

x = (84^(1/2)-4)/(1*2) or x = (-84^(1/2)-4)/(1*2)

x = (2*21^(1/2)-4)/2 or x = (-2*21^(1/2)-4)/2

x in { (-2*21^(1/2)-4)/2, (2*21^(1/2)-4)/2, 8} 

(x-((-2*21^(1/2)-4)/2))*(x-((2*21^(1/2)-4)/2))*(x-8) = 0

((x-((-2*21^(1/2)-4)/2))*(x-((2*21^(1/2)-4)/2))*(x-8))/(2*(x-1)*(x-7)) = 0

((x-((-2*21^(1/2)-4)/2))*(x-((2*21^(1/2)-4)/2))*(x-8))/(2*(x-1)*(x-7)) = 0 // * 2*(x-1)*(x-7)

(x-((-2*21^(1/2)-4)/2))*(x-((2*21^(1/2)-4)/2))*(x-8) = 0

( x-((-2*21^(1/2)-4)/2) )

x-((-2*21^(1/2)-4)/2) = 0 // + (-2*21^(1/2)-4)/2

x = (-2*21^(1/2)-4)/2

( x-((2*21^(1/2)-4)/2) )

x-((2*21^(1/2)-4)/2) = 0 // + (2*21^(1/2)-4)/2

x = (2*21^(1/2)-4)/2

( x-8 )

x-8 = 0 // + 8

x = 8

x in { (-2*21^(1/2)-4)/2, (2*21^(1/2)-4)/2, 8 }

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