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

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


D( x )

x+2 = 0

x^2-4 = 0

x+2 = 0

x+2 = 0

x+2 = 0 // - 2

x = -2

x^2-4 = 0

x^2-4 = 0

1*x^2 = 4 // : 1

x^2 = 4

x^2 = 4 // ^ 1/2

abs(x) = 2

x = 2 or x = -2

x in (-oo:-2) U (-2:2) U (2:+oo)

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

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

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

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

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

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

8*x^2-12*x-32-24 = 0

8*x^2-12*x-56 = 0

8*x^2-12*x-56 = 0

4*(2*x^2-3*x-14) = 0

2*x^2-3*x-14 = 0

DELTA = (-3)^2-(-14*2*4)

DELTA = 121

DELTA > 0

x = (121^(1/2)+3)/(2*2) or x = (3-121^(1/2))/(2*2)

x = 7/2 or x = -2

4*(x+2)*(x-7/2) = 0

(4*(x+2)*(x-7/2))/((x+2)*(x^2-4)) = 0

(4*(x+2)*(x-7/2))/((x+2)*(x^2-4)) = 0 // * (x+2)*(x^2-4)

4*(x+2)*(x-7/2) = 0

( x+2 )

x+2 = 0 // - 2

x = -2

( x-7/2 )

x-7/2 = 0 // + 7/2

x = 7/2

x in { -2} 

x = 7/2

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