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

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


D( y )

y+3 = 0

y+2 = 0

y+3 = 0

y+3 = 0

y+3 = 0 // - 3

y = -3

y+2 = 0

y+2 = 0

y+2 = 0 // - 2

y = -2

y in (-oo:-3) U (-3:-2) U (-2:+oo)

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

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

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

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

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

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

4*y^2-8*y+20*y-19+24 = 0

4*y^2+12*y+5 = 0

4*y^2+12*y+5 = 0

4*y^2+12*y+5 = 0

DELTA = 12^2-(4*4*5)

DELTA = 64

DELTA > 0

y = (64^(1/2)-12)/(2*4) or y = (-64^(1/2)-12)/(2*4)

y = -1/2 or y = -5/2

(y+5/2)*(y+1/2) = 0

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

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

(y+5/2)*(y+1/2) = 0

( y+1/2 )

y+1/2 = 0 // - 1/2

y = -1/2

( y+5/2 )

y+5/2 = 0 // - 5/2

y = -5/2

y in { -1/2, -5/2 }

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