(5p/3p)-((p+3)/(3p-12))

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Solution for (5p/3p)-((p+3)/(3p-12)) equation:


D( p )

3*p-12 = 0

3*p-12 = 0

3*p-12 = 0

3*p-12 = 0 // + 12

3*p = 12 // : 3

p = 12/3

p = 4

p in (-oo:4) U (4:+oo)

t_1 = 0

5/3*p^2-((p+3)/(3*p-12))+t_1 = 0

(-1*(p+3))/(3*p-12)+(5*p^2)/3+t_1 = 0

(-1*3*(p+3))/(3*(3*p-12))+(5*p^2*(3*p-12))/(3*(3*p-12))+(3*t_1*(3*p-12))/(3*(3*p-12)) = 0

5*p^2*(3*p-12)-1*3*(p+3)+3*t_1*(3*p-12) = 0

15*p^3-60*p^2-3*p+9*p*t_1-36*t_1-9 = 0

15*p^3-60*p^2-3*p+9*p*t_1-36*t_1-9 = 0

3*(5*p^3-20*p^2-p+3*p*t_1-12*t_1-3) = 0

5*p^3-20*p^2-p+3*p*t_1-12*t_1-3

p*(5*p^2-1)-20*p^2+3*p*t_1-12*t_1-3

p*(5*p^2-1)-3*(4*t_1+1)-20*p^2+3*p*t_1

p*(3*t_1-20*p)-3*(4*t_1+1)+p*(5*p^2-1)

p*(5*p^2-20*p+3*t_1-1)-3*(4*t_1+1)

-2*(5*p^2-20*p+3*t_1-1)

-2*3*(5*p^2-20*p+3*t_1-1) = 0

(-2*3*(5*p^2-20*p+3*t_1-1))/(3*(3*p-12)) = 0

(-2*3*(5*p^2-20*p+3*t_1-1))/(3*(3*p-12)) = 0 // * 3*(3*p-12)

-2*3*(5*p^2-20*p+3*t_1-1) = 0

5*p^2-20*p+3*t_1-1 = 0

DELTA = (-20)^2-(4*5*(3*t_1-1))

DELTA = 400-20*(3*t_1-1)

400-20*(3*t_1-1) = 0

400-20*(3*t_1-1) = 0

420-60*t_1 = 0

420-60*t_1 = 0

420-60*t_1 = 0 // - 420

-60*t_1 = -420 // : -60

t_1 = -420/(-60)

t_1 = 7

DELTA = 0 <=> t_3 = 7

p = 20/(2*5) i t_1 = 7

p = 2 i t_1 = 7

( p = ((400-20*(3*t_1-1))^(1/2)+20)/(2*5) or p = (20-(400-20*(3*t_1-1))^(1/2))/(2*5) ) i t_1 > 7

( p = ((400-20*(3*t_1-1))^(1/2)+20)/10 or p = (20-(400-20*(3*t_1-1))^(1/2))/10 ) i t_1 > 7

t_1-7 > 0

t_1-7 > 0 // + 7

t_1 > 7

p in { 2, ((400-20*(0*3-1))^(1/2)+20)/10, (20-(400-20*(0*3-1))^(1/2))/10 }

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