(3y+1)/(y)=(2y-5)/(y-4)

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Solution for (3y+1)/(y)=(2y-5)/(y-4) equation:


D( y )

y = 0

y-4 = 0

y = 0

y = 0

y-4 = 0

y-4 = 0

y-4 = 0 // + 4

y = 4

y in (-oo:0) U (0:4) U (4:+oo)

(3*y+1)/y = (2*y-5)/(y-4) // - (2*y-5)/(y-4)

(3*y+1)/y-((2*y-5)/(y-4)) = 0

(3*y+1)/y+(-1*(2*y-5))/(y-4) = 0

((3*y+1)*(y-4))/(y*(y-4))+(-1*y*(2*y-5))/(y*(y-4)) = 0

(3*y+1)*(y-4)-1*y*(2*y-5) = 0

y^2-6*y-4 = 0

y^2-6*y-4 = 0

y^2-6*y-4 = 0

DELTA = (-6)^2-(-4*1*4)

DELTA = 52

DELTA > 0

y = (52^(1/2)+6)/(1*2) or y = (6-52^(1/2))/(1*2)

y = (2*13^(1/2)+6)/2 or y = (6-2*13^(1/2))/2

(y-((6-2*13^(1/2))/2))*(y-((2*13^(1/2)+6)/2)) = 0

((y-((6-2*13^(1/2))/2))*(y-((2*13^(1/2)+6)/2)))/(y*(y-4)) = 0

((y-((6-2*13^(1/2))/2))*(y-((2*13^(1/2)+6)/2)))/(y*(y-4)) = 0 // * y*(y-4)

(y-((6-2*13^(1/2))/2))*(y-((2*13^(1/2)+6)/2)) = 0

( y-((2*13^(1/2)+6)/2) )

y-((2*13^(1/2)+6)/2) = 0 // + (2*13^(1/2)+6)/2

y = (2*13^(1/2)+6)/2

( y-((6-2*13^(1/2))/2) )

y-((6-2*13^(1/2))/2) = 0 // + (6-2*13^(1/2))/2

y = (6-2*13^(1/2))/2

y in { (2*13^(1/2)+6)/2, (6-2*13^(1/2))/2 }

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