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

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


D( y )

3*y+2 = 0

4*y-1 = 0

3*y+2 = 0

3*y+2 = 0

3*y+2 = 0 // - 2

3*y = -2 // : 3

y = -2/3

4*y-1 = 0

4*y-1 = 0

4*y-1 = 0 // + 1

4*y = 1 // : 4

y = 1/4

y in (-oo:-2/3) U (-2/3:1/4) U (1/4:+oo)

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

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

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

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

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

24*y-6*y^2+4 = 0

24*y-6*y^2+4 = 0

2*(12*y-3*y^2+2) = 0

12*y-3*y^2+2 = 0

DELTA = 12^2-(-3*2*4)

DELTA = 168

DELTA > 0

y = (168^(1/2)-12)/(-3*2) or y = (-168^(1/2)-12)/(-3*2)

y = (2*42^(1/2)-12)/(-6) or y = (-2*42^(1/2)-12)/(-6)

2*(y-((2*42^(1/2)-12)/(-6)))*(y-((-2*42^(1/2)-12)/(-6))) = 0

(2*(y-((2*42^(1/2)-12)/(-6)))*(y-((-2*42^(1/2)-12)/(-6))))/((4*y-1)*(3*y+2)) = 0

(2*(y-((2*42^(1/2)-12)/(-6)))*(y-((-2*42^(1/2)-12)/(-6))))/((4*y-1)*(3*y+2)) = 0 // * (4*y-1)*(3*y+2)

2*(y-((2*42^(1/2)-12)/(-6)))*(y-((-2*42^(1/2)-12)/(-6))) = 0

( y-((-2*42^(1/2)-12)/(-6)) )

y-((-2*42^(1/2)-12)/(-6)) = 0 // + (-2*42^(1/2)-12)/(-6)

y = (-2*42^(1/2)-12)/(-6)

( y-((2*42^(1/2)-12)/(-6)) )

y-((2*42^(1/2)-12)/(-6)) = 0 // + (2*42^(1/2)-12)/(-6)

y = (2*42^(1/2)-12)/(-6)

y in { (-2*42^(1/2)-12)/(-6), (2*42^(1/2)-12)/(-6) }

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