2/(x+3)+(3/8)=5/(4x+12)

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Solution for 2/(x+3)+(3/8)=5/(4x+12) equation: 


D( x )

x+3 = 0

4*x+12 = 0

x+3 = 0

x+3 = 0

x+3 = 0 // - 3

x = -3

4*x+12 = 0

4*x+12 = 0

4*x+12 = 0 // - 12

4*x = -12 // : 4

x = -12/4

x = -3

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

2/(x+3)+3/8 = 5/(4*x+12) // - 5/(4*x+12)

2/(x+3)-(5/(4*x+12))+3/8 = 0

2/(x+3)-5*(4*x+12)^-1+3/8 = 0

2/(x+3)-5/(4*x+12)+3/8 = 0

(2*8*(4*x+12))/(8*(x+3)*(4*x+12))+(-5*8*(x+3))/(8*(x+3)*(4*x+12))+(3*(x+3)*(4*x+12))/(8*(x+3)*(4*x+12)) = 0

2*8*(4*x+12)-5*8*(x+3)+3*(x+3)*(4*x+12) = 0

12*x^2+24*x+72*x+72+108 = 0

12*x^2+96*x+180 = 0

12*x^2+96*x+180 = 0

12*(x^2+8*x+15) = 0

x^2+8*x+15 = 0

DELTA = 8^2-(1*4*15)

DELTA = 4

DELTA > 0

x = (4^(1/2)-8)/(1*2) or x = (-4^(1/2)-8)/(1*2)

x = -3 or x = -5

12*(x+5)*(x+3) = 0

(12*(x+5)*(x+3))/(8*(x+3)*(4*x+12)) = 0

(12*(x+5)*(x+3))/(8*(x+3)*(4*x+12)) = 0 // * 8*(x+3)*(4*x+12)

12*(x+5)*(x+3) = 0

( x+3 )

x+3 = 0 // - 3

x = -3

( x+5 )

x+5 = 0 // - 5

x = -5

x in { -3} 

x = -5

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