(4/(x+4))-(3/(x-4))=(2x/((x^2)-16))

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Solution for (4/(x+4))-(3/(x-4))=(2x/((x^2)-16)) equation: 


D( x )

x^2-16 = 0

x+4 = 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-4 = 0

x-4 = 0

x-4 = 0 // + 4

x = 4

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

4/(x+4)-(3/(x-4)) = (2*x)/(x^2-16) // - (2*x)/(x^2-16)

4/(x+4)-(3/(x-4))-((2*x)/(x^2-16)) = 0

4/(x+4)-3*(x-4)^-1-2*x*(x^2-16)^-1 = 0

4/(x+4)-3/(x-4)+(-2*x)/(x^2-16) = 0

(4*(x-4)*(x^2-16))/((x+4)*(x-4)*(x^2-16))+(-3*(x+4)*(x^2-16))/((x+4)*(x-4)*(x^2-16))+(-2*x*(x+4)*(x-4))/((x+4)*(x-4)*(x^2-16)) = 0

4*(x-4)*(x^2-16)-3*(x+4)*(x^2-16)-2*x*(x+4)*(x-4) = 0

x^3-2*x^3-28*x^2-16*x+32*x+448 = 0

16*x-x^3-28*x^2+448 = 0

16*x-x^3-28*x^2+448 = 0

16*x-x^3-28*x^2+448

28*(16-x^2)-x^3+16*x

x*(16-x^2)+28*(16-x^2)

(x+28)*(16-x^2)

((x+28)*(16-x^2))/((x+4)*(x-4)*(x^2-16)) = 0

((x+28)*(16-x^2))/((x+4)*(x-4)*(x^2-16)) = 0 // * (x+4)*(x-4)*(x^2-16)

(x+28)*(16-x^2) = 0

( 16-x^2 )

-1*x^2 = -16 // : -1

x^2 = 16

x^2 = 16 // ^ 1/2

abs(x) = 4

x = 4 or x = -4

( x+28 )

x+28 = 0 // - 28

x = -28

x in { 4} 

x in { -4} 

x = -28

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