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

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


D( q )

q+4 = 0

3*q-2 = 0

q+4 = 0

q+4 = 0

q+4 = 0 // - 4

q = -4

3*q-2 = 0

3*q-2 = 0

3*q-2 = 0 // + 2

3*q = 2 // : 3

q = 2/3

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

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

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

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

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

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

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

3*q^2+3*q^2-6*q+10*q-16-8 = 0

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

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

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

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

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

DELTA = 148

DELTA > 0

q = (148^(1/2)-2)/(2*3) or q = (-148^(1/2)-2)/(2*3)

q = (2*37^(1/2)-2)/6 or q = (-2*37^(1/2)-2)/6

2*(q-((-2*37^(1/2)-2)/6))*(q-((2*37^(1/2)-2)/6)) = 0

(2*(q-((-2*37^(1/2)-2)/6))*(q-((2*37^(1/2)-2)/6)))/((q+4)*(3*q-2)) = 0

(2*(q-((-2*37^(1/2)-2)/6))*(q-((2*37^(1/2)-2)/6)))/((q+4)*(3*q-2)) = 0 // * (q+4)*(3*q-2)

2*(q-((-2*37^(1/2)-2)/6))*(q-((2*37^(1/2)-2)/6)) = 0

( q-((-2*37^(1/2)-2)/6) )

q-((-2*37^(1/2)-2)/6) = 0 // + (-2*37^(1/2)-2)/6

q = (-2*37^(1/2)-2)/6

( q-((2*37^(1/2)-2)/6) )

q-((2*37^(1/2)-2)/6) = 0 // + (2*37^(1/2)-2)/6

q = (2*37^(1/2)-2)/6

q in { (-2*37^(1/2)-2)/6, (2*37^(1/2)-2)/6 }

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