5/(x-2)+(x+3)

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Solution for 5/(x-2)+(x+3) equation: 


D( x )

x-2 = 0

x-2 = 0

x-2 = 0

x-2 = 0 // + 2

x = 2

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

5/(x-2)+x+3 = 0

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

x*(x-2)+3*(x-2)+5 = 0

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

x^2+x-1 = 0

x^2+x-1 = 0

x^2+x-1 = 0

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

DELTA = 5

DELTA > 0

x = (5^(1/2)-1)/(1*2) or x = (-5^(1/2)-1)/(1*2)

x = (5^(1/2)-1)/2 or x = (-(5^(1/2)+1))/2

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

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

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

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

( x+(5^(1/2)+1)/2 )

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

x = -((5^(1/2)+1)/2)

( x-((5^(1/2)-1)/2) )

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

x = (5^(1/2)-1)/2

x in { -((5^(1/2)+1)/2), (5^(1/2)-1)/2 }

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