4/(5x+15)-1/(x+3)=3/5

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Solution for 4/(5x+15)-1/(x+3)=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)

4/(5*x+15)-(1/(x+3)) = 3/5 // - 3/5

4/(5*x+15)-(1/(x+3))-(3/5) = 0

4/(5*x+15)-(x+3)^-1-3/5 = 0

4/(5*x+15)-1/(x+3)-3/5 = 0

(4*5*(x+3))/(5*(5*x+15)*(x+3))+(-1*5*(5*x+15))/(5*(5*x+15)*(x+3))+(-3*(5*x+15)*(x+3))/(5*(5*x+15)*(x+3)) = 0

4*5*(x+3)-1*5*(5*x+15)-3*(5*x+15)*(x+3) = 0

-15*x^2-5*x-90*x-135-15 = 0

-15*x^2-95*x-150 = 0

-15*x^2-95*x-150 = 0

-5*(3*x^2+19*x+30) = 0

3*x^2+19*x+30 = 0

DELTA = 19^2-(3*4*30)

DELTA = 1

DELTA > 0

x = (1^(1/2)-19)/(2*3) or x = (-1^(1/2)-19)/(2*3)

x = -3 or x = -10/3

-5*(x+10/3)*(x+3) = 0

(-5*(x+10/3)*(x+3))/(5*(5*x+15)*(x+3)) = 0

(-5*(x+10/3)*(x+3))/(5*(5*x+15)*(x+3)) = 0 // * 5*(5*x+15)*(x+3)

-5*(x+10/3)*(x+3) = 0

( x+10/3 )

x+10/3 = 0 // - 10/3

x = -10/3

( x+3 )

x+3 = 0 // - 3

x = -3

x in { -3} 

x = -10/3

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