(4-2x)+2/(3+x)=5/p

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


D( x )

x+3 = 0

x+3 = 0

x+3 = 0

x+3 = 0 // - 3

x = -3

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

t_1 = 4-5*p^-1

2/(x+3)+t_1-2*x = 0

2/(x+3)+(t_1*(x+3))/(x+3)+(-2*x*(x+3))/(x+3) = 0

t_1*(x+3)-2*x*(x+3)+2 = 0

t_1*x+3*t_1-2*x^2-6*x+2 = 0

(t_1*x+3*t_1-2*x^2-6*x+2)/(x+3) = 0

(t_1*x+3*t_1-2*x^2-6*x+2)/(x+3) = 0 // * x+3

t_1*x+3*t_1-2*x^2-6*x+2 = 0

3*t_1-2*x^2-6*x+2 = 0

DELTA = (-6)^2-(-2*4*(3*t_1+2))

DELTA = 8*(3*t_1+2)+36

8*(3*t_1+2)+36 = 0

8*(3*t_1+2)+36 = 0

24*t_1+52 = 0

24*t_1+52 = 0

24*t_1+52 = 0 // - 52

24*t_1 = -52 // : 24

t_1 = -52/24

t_1 = -13/6

DELTA = 0  <=>  t_4 = -13/6

x = 6/(-2*2) i t_1 = -13/6

x = -3/2 i t_1 = -13/6

( x = ((8*(3*t_1+2)+36)^(1/2)+6)/(-2*2) or x = (6-(8*(3*t_1+2)+36)^(1/2))/(-2*2) ) i t_1 > -13/6

( x = ((8*(3*t_1+2)+36)^(1/2)+6)/(-4) or x = (6-(8*(3*t_1+2)+36)^(1/2))/(-4) ) i t_1 > -13/6

t_1+13/6 > 0

t_1+13/6 > 0 // - 13/6

t_1 > -13/6

x in { -3/2, ((8*(3*(4-5*p^-1)+2)+36)^(1/2)+6)/(-4), (6-(8*(3*(4-5*p^-1)+2)+36)^(1/2))/(-4) }

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