1/(5x+15)-3/(x+3)=5

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Solution for 1/(5x+15)-3/(x+3)=5 equation: 


D( x )

5*x+15 = 0

x+3 = 0

5*x+15 = 0

5*x+15 = 0

5*x+15 = 0 // - 15

5*x = -15 // : 5

x = -15/5

x = -3

x+3 = 0

x+3 = 0

x+3 = 0 // - 3

x = -3

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

1/(5*x+15)-(3/(x+3)) = 5 // - 5

1/(5*x+15)-(3/(x+3))-5 = 0

1/(5*x+15)-3*(x+3)^-1-5 = 0

1/(5*x+15)-3/(x+3)-5 = 0

(1*(x+3))/((5*x+15)*(x+3))+(-3*(5*x+15))/((5*x+15)*(x+3))+(-5*(5*x+15)*(x+3))/((5*x+15)*(x+3)) = 0

1*(x+3)-3*(5*x+15)-5*(5*x+15)*(x+3) = 0

-25*x^2-14*x-150*x-225-42 = 0

-25*x^2-164*x-267 = 0

-25*x^2-164*x-267 = 0

-1*(25*x^2+164*x+267) = 0

25*x^2+164*x+267 = 0

DELTA = 164^2-(4*25*267)

DELTA = 196

DELTA > 0

x = (196^(1/2)-164)/(2*25) or x = (-196^(1/2)-164)/(2*25)

x = -3 or x = -89/25

-1*(x+89/25)*(x+3) = 0

(-1*(x+89/25)*(x+3))/((5*x+15)*(x+3)) = 0

(-1*(x+89/25)*(x+3))/((5*x+15)*(x+3)) = 0 // * (5*x+15)*(x+3)

-1*(x+89/25)*(x+3) = 0

( x+3 )

x+3 = 0 // - 3

x = -3

( x+89/25 )

x+89/25 = 0 // - 89/25

x = -89/25

x in { -3} 

x = -89/25

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