(30/(x+1)(x+4))+(10/(x+4))=(4/(x+1))

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Solution for (30/(x+1)(x+4))+(10/(x+4))=(4/(x+1)) equation: 


D( x )

x+4 = 0

x+1 = 0

x+4 = 0

x+4 = 0

x+4 = 0 // - 4

x = -4

x+1 = 0

x+1 = 0

x+1 = 0 // - 1

x = -1

x in (-oo:-4) U (-4:-1) U (-1:+oo)

(30/(x+1))*(x+4)+10/(x+4) = 4/(x+1) // - 4/(x+1)

(30/(x+1))*(x+4)+10/(x+4)-(4/(x+1)) = 0

(30/(x+1))*(x+4)+10/(x+4)-4*(x+1)^-1 = 0

(30*(x+4))/(x+1)+10/(x+4)-4/(x+1) = 0

(30*(x+4)^2)/((x+1)*(x+4))+(10*(x+1))/((x+1)*(x+4))+(-4*(x+4))/((x+1)*(x+4)) = 0

30*(x+4)^2+10*(x+1)-4*(x+4) = 0

30*x^2+250*x-4*x-16+490 = 0

30*x^2+246*x+474 = 0

30*x^2+246*x+474 = 0

6*(5*x^2+41*x+79) = 0

5*x^2+41*x+79 = 0

DELTA = 41^2-(4*5*79)

DELTA = 101

DELTA > 0

x = (101^(1/2)-41)/(2*5) or x = (-101^(1/2)-41)/(2*5)

x = (101^(1/2)-41)/10 or x = (-(101^(1/2)+41))/10

6*(x+(101^(1/2)+41)/10)*(x-((101^(1/2)-41)/10)) = 0

(6*(x+(101^(1/2)+41)/10)*(x-((101^(1/2)-41)/10)))/((x+1)*(x+4)) = 0

(6*(x+(101^(1/2)+41)/10)*(x-((101^(1/2)-41)/10)))/((x+1)*(x+4)) = 0 // * (x+1)*(x+4)

6*(x+(101^(1/2)+41)/10)*(x-((101^(1/2)-41)/10)) = 0

( x+(101^(1/2)+41)/10 )

x+(101^(1/2)+41)/10 = 0 // - (101^(1/2)+41)/10

x = -((101^(1/2)+41)/10)

( x-((101^(1/2)-41)/10) )

x-((101^(1/2)-41)/10) = 0 // + (101^(1/2)-41)/10

x = (101^(1/2)-41)/10

x in { -((101^(1/2)+41)/10), (101^(1/2)-41)/10 }

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