What are the roots of the equation x / (x + 2) + 3 / (x - 4).

Let f(x) = x/(x+2)  +
3/(x-4)

To find the roots, we will rewrite as one
fraction.

==> f(x)= [ x(x-4) + 3(x+2) ] /
(x+2)(x-4)

==> f(x) = ( x^2 - 4x + 3x + 6) /
(x+2)(x-4)

==> f(x) = (x^2 -x + 6) /
(x+2)(x-4)

Now the roots if f(x) are the roots of the
numerator.

=> x^2 -x + 6 =
0

==> x1= ( 1 + sqrt(1 - 24) /2 = (1/2) + sqrt23 /
2

==> x2= (1/2) - sqrt23*i
/2

Then the roots
are:

x = { (1/2) + (sqrt23 /2) *i  and (1/2)
- (sqrt23 /2)*i }