1/(x-5)-3(x+2)=7/(x*x-3*x-10)

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Solution for 1/(x-5)-3(x+2)=7/(x*x-3*x-10) equation: 


D( x )

x-5 = 0

x*x-(3*x)-10 = 0

x-5 = 0

x-5 = 0

x-5 = 0 // + 5

x = 5

x*x-(3*x)-10 = 0

x*x-(3*x)-10 = 0

x*x-3*x-10 = 0

x^2-3*x-10 = 0

DELTA = (-3)^2-(-10*1*4)

DELTA = 49

DELTA > 0

x = (49^(1/2)+3)/(1*2) or x = (3-49^(1/2))/(1*2)

x = 5 or x = -2

x in (-oo:-2) U (-2:5) U (5:+oo)

1/(x-5)-(3*(x+2)) = 7/(x*x-(3*x)-10) // - 7/(x*x-(3*x)-10)

1/(x-5)-(3*(x+2))-(7/(x*x-(3*x)-10)) = 0

1/(x-5)-3*(x+2)-7*(x*x-3*x-10)^-1 = 0

1/(x-5)-3*(x+2)-7/(x^2-3*x-10) = 0

x^2-3*x-10 = 0

x^2-3*x-10 = 0

x^2-3*x-10 = 0

DELTA = (-3)^2-(-10*1*4)

DELTA = 49

DELTA > 0

x = (49^(1/2)+3)/(1*2) or x = (3-49^(1/2))/(1*2)

x = 5 or x = -2

(x+2)*(x-5) = 0

1/(x-5)-3*(x+2)-7/((x+2)*(x-5)) = 0

(1*(x+2))/((x-5)*(x+2))+(-3*(x+2)^2*(x-5))/((x-5)*(x+2))-7/((x-5)*(x+2)) = 0

1*(x+2)-3*(x+2)^2*(x-5)-7 = 0

3*x^2-3*x^3+49*x-7+62 = 0

3*x^2-3*x^3+49*x+55 = 0

3*x^2-3*x^3+49*x+55 = 0

3*x^2-3*x^3+49*x+55 = 0

{ 1, -1, 5, -5, 11, -11, 55, -55 }

1

x = 1

3*x^2-3*x^3+49*x+55 = 104

1

-1

x = -1

3*x^2-3*x^3+49*x+55 = 12

-1

5

x = 5

3*x^2-3*x^3+49*x+55 = 0

5

x-5

-3*x^2-12*x-11

3*x^2-3*x^3+49*x+55

x-5

3*x^3-15*x^2

49*x-12*x^2+55

12*x^2-60*x

55-11*x

11*x-55

0

-3*x^2-12*x-11 = 0

DELTA = (-12)^2-(-11*(-3)*4)

DELTA = 12

DELTA > 0

x = (12^(1/2)+12)/(-3*2) or x = (12-12^(1/2))/(-3*2)

x = (2*3^(1/2)+12)/(-6) or x = (12-2*3^(1/2))/(-6)

x in { (2*3^(1/2)+12)/(-6), (12-2*3^(1/2))/(-6), 5} 

(x-((2*3^(1/2)+12)/(-6)))*(x-((12-2*3^(1/2))/(-6)))*(x-5) = 0

((x-((2*3^(1/2)+12)/(-6)))*(x-((12-2*3^(1/2))/(-6)))*(x-5))/((x-5)*(x+2)) = 0

((x-((2*3^(1/2)+12)/(-6)))*(x-((12-2*3^(1/2))/(-6)))*(x-5))/((x-5)*(x+2)) = 0 // * (x-5)*(x+2)

(x-((2*3^(1/2)+12)/(-6)))*(x-((12-2*3^(1/2))/(-6)))*(x-5) = 0

( x-((12-2*3^(1/2))/(-6)) )

x-((12-2*3^(1/2))/(-6)) = 0 // + (12-2*3^(1/2))/(-6)

x = (12-2*3^(1/2))/(-6)

( x-((2*3^(1/2)+12)/(-6)) )

x-((2*3^(1/2)+12)/(-6)) = 0 // + (2*3^(1/2)+12)/(-6)

x = (2*3^(1/2)+12)/(-6)

( x-5 )

x-5 = 0 // + 5

x = 5

x in { 5} 

x in { (12-2*3^(1/2))/(-6), (2*3^(1/2)+12)/(-6) }

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