5/(x+4)+4/(x^2-16)

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Solution for 5/(x+4)+4/(x^2-16) equation: 


D( x )

x^2-16 = 0

x+4 = 0

x^2-16 = 0

x^2-16 = 0

1*x^2 = 16 // : 1

x^2 = 16

x^2 = 16 // ^ 1/2

abs(x) = 4

x = 4 or x = -4

x+4 = 0

x+4 = 0

x+4 = 0 // - 4

x = -4

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

5/(x+4)+4/(x^2-16) = 0

(5*(x^2-16))/((x+4)*(x^2-16))+(4*(x+4))/((x+4)*(x^2-16)) = 0

5*(x^2-16)+4*(x+4) = 0

5*x^2+4*x-64 = 0

5*x^2+4*x-64 = 0

5*x^2+4*x-64 = 0

DELTA = 4^2-(-64*4*5)

DELTA = 1296

DELTA > 0

x = (1296^(1/2)-4)/(2*5) or x = (-1296^(1/2)-4)/(2*5)

x = 16/5 or x = -4

(x+4)*(x-16/5) = 0

((x+4)*(x-16/5))/((x+4)*(x^2-16)) = 0

((x+4)*(x-16/5))/((x+4)*(x^2-16)) = 0 // * (x+4)*(x^2-16)

(x+4)*(x-16/5) = 0

( x+4 )

x+4 = 0 // - 4

x = -4

( x-16/5 )

x-16/5 = 0 // + 16/5

x = 16/5

x in { -4} 

x = 16/5

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