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

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


D( x )

x-5 = 0

x = 0

x-5 = 0

x-5 = 0

x-5 = 0 // + 5

x = 5

x = 0

x = 0

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

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

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

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

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

15*x-6*x^2+30*x-40 = 0

45*x-6*x^2-40 = 0

45*x-6*x^2-40 = 0

45*x-6*x^2-40 = 0

DELTA = 45^2-(-40*(-6)*4)

DELTA = 1065

DELTA > 0

x = (1065^(1/2)-45)/(-6*2) or x = (-1065^(1/2)-45)/(-6*2)

x = (1065^(1/2)-45)/(-12) or x = (1065^(1/2)+45)/12

(x-((1065^(1/2)-45)/(-12)))*(x-((1065^(1/2)+45)/12)) = 0

((x-((1065^(1/2)-45)/(-12)))*(x-((1065^(1/2)+45)/12)))/(x*(x-5)) = 0

((x-((1065^(1/2)-45)/(-12)))*(x-((1065^(1/2)+45)/12)))/(x*(x-5)) = 0 // * x*(x-5)

(x-((1065^(1/2)-45)/(-12)))*(x-((1065^(1/2)+45)/12)) = 0

( x-((1065^(1/2)+45)/12) )

x-((1065^(1/2)+45)/12) = 0 // + (1065^(1/2)+45)/12

x = (1065^(1/2)+45)/12

( x-((1065^(1/2)-45)/(-12)) )

x-((1065^(1/2)-45)/(-12)) = 0 // + (1065^(1/2)-45)/(-12)

x = (1065^(1/2)-45)/(-12)

x in { (1065^(1/2)+45)/12, (1065^(1/2)-45)/(-12) }

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