(5/(2x-10))+2=-6/(x-5)

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Solution for (5/(2x-10))+2=-6/(x-5) equation: 


D( x )

x-5 = 0

2*x-10 = 0

x-5 = 0

x-5 = 0

x-5 = 0 // + 5

x = 5

2*x-10 = 0

2*x-10 = 0

2*x-10 = 0 // + 10

2*x = 10 // : 2

x = 10/2

x = 5

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

5/(2*x-10)+2 = -6/(x-5) // + -6/(x-5)

5/(2*x-10)-(-6/(x-5))+2 = 0

5/(2*x-10)+6*(x-5)^-1+2 = 0

5/(2*x-10)+6/(x-5)+2 = 0

(5*(x-5))/((2*x-10)*(x-5))+(6*(2*x-10))/((2*x-10)*(x-5))+(2*(2*x-10)*(x-5))/((2*x-10)*(x-5)) = 0

5*(x-5)+6*(2*x-10)+2*(2*x-10)*(x-5) = 0

4*x^2+17*x-40*x-85+100 = 0

4*x^2-23*x+15 = 0

4*x^2-23*x+15 = 0

4*x^2-23*x+15 = 0

DELTA = (-23)^2-(4*4*15)

DELTA = 289

DELTA > 0

x = (289^(1/2)+23)/(2*4) or x = (23-289^(1/2))/(2*4)

x = 5 or x = 3/4

(x-3/4)*(x-5) = 0

((x-3/4)*(x-5))/((2*x-10)*(x-5)) = 0

((x-3/4)*(x-5))/((2*x-10)*(x-5)) = 0 // * (2*x-10)*(x-5)

(x-3/4)*(x-5) = 0

( x-3/4 )

x-3/4 = 0 // + 3/4

x = 3/4

( x-5 )

x-5 = 0 // + 5

x = 5

x in { 5} 

x = 3/4

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