(-5/(2v-6))+4=6/(v-3)

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Solution for (-5/(2v-6))+4=6/(v-3) equation:


D( v )

v-3 = 0

2*v-6 = 0

v-3 = 0

v-3 = 0

v-3 = 0 // + 3

v = 3

2*v-6 = 0

2*v-6 = 0

2*v-6 = 0 // + 6

2*v = 6 // : 2

v = 6/2

v = 3

v in (-oo:3) U (3:+oo)

4-5/(2*v-6) = 6/(v-3) // - 6/(v-3)

4-5/(2*v-6)-(6/(v-3)) = 0

4-5/(2*v-6)-6*(v-3)^-1 = 0

4-5/(2*v-6)-6/(v-3) = 0

(-5*(v-3))/((2*v-6)*(v-3))+(-6*(2*v-6))/((2*v-6)*(v-3))+(4*(2*v-6)*(v-3))/((2*v-6)*(v-3)) = 0

4*(2*v-6)*(v-3)-5*(v-3)-6*(2*v-6) = 0

8*v^2-17*v-48*v+51+72 = 0

8*v^2-65*v+123 = 0

8*v^2-65*v+123 = 0

8*v^2-65*v+123 = 0

DELTA = (-65)^2-(4*8*123)

DELTA = 289

DELTA > 0

v = (289^(1/2)+65)/(2*8) or v = (65-289^(1/2))/(2*8)

v = 41/8 or v = 3

(v-3)*(v-41/8) = 0

((v-3)*(v-41/8))/((2*v-6)*(v-3)) = 0

((v-3)*(v-41/8))/((2*v-6)*(v-3)) = 0 // * (2*v-6)*(v-3)

(v-3)*(v-41/8) = 0

( v-3 )

v-3 = 0 // + 3

v = 3

( v-41/8 )

v-41/8 = 0 // + 41/8

v = 41/8

v in { 3}

v = 41/8

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