-4/(v-5)=1/(2v-10)+2

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Solution for -4/(v-5)=1/(2v-10)+2 equation: 


D( v )

v-5 = 0

2*v-10 = 0

v-5 = 0

v-5 = 0

v-5 = 0 // + 5

v = 5

2*v-10 = 0

2*v-10 = 0

2*v-10 = 0 // + 10

2*v = 10 // : 2

v = 10/2

v = 5

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

-4/(v-5) = 1/(2*v-10)+2 // - 1/(2*v-10)+2

-4/(v-5)-(1/(2*v-10))-2 = 0

-4/(v-5)-(2*v-10)^-1-2 = 0

-4/(v-5)-1/(2*v-10)-2 = 0

(-4*(2*v-10))/((v-5)*(2*v-10))+(-1*(v-5))/((v-5)*(2*v-10))+(-2*(v-5)*(2*v-10))/((v-5)*(2*v-10)) = 0

-4*(2*v-10)-1*(v-5)-2*(v-5)*(2*v-10) = 0

40*v-4*v^2-9*v-100+45 = 0

31*v-4*v^2-55 = 0

31*v-4*v^2-55 = 0

31*v-4*v^2-55 = 0

DELTA = 31^2-(-55*(-4)*4)

DELTA = 81

DELTA > 0

v = (81^(1/2)-31)/(-4*2) or v = (-81^(1/2)-31)/(-4*2)

v = 11/4 or v = 5

(v-11/4)*(v-5) = 0

((v-11/4)*(v-5))/((v-5)*(2*v-10)) = 0

((v-11/4)*(v-5))/((v-5)*(2*v-10)) = 0 // * (v-5)*(2*v-10)

(v-11/4)*(v-5) = 0

( v-11/4 )

v-11/4 = 0 // + 11/4

v = 11/4

( v-5 )

v-5 = 0 // + 5

v = 5

v in { 5} 

v = 11/4

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