Question

How do you solve `1/(x^2 -3) = 8/x`?

Answer 1

`x=1/16+-sqrt(769)/16`

Explanation:

Multiply both sides by `x(x^2-3)` to get:

`x = 8(x^2-3) = 8x^2-24`

Subtract `x` from both sides and transpose to get:

`8x^2-x-24 = 0`

This is in the form `ax^2+bx+c = 0` with `a=8`, `b=-1` and `c=-24`, which has roots given by the quadratic formula:

`x = (-b+-sqrt(b^2-4ac))/(2a)`

`=(1+-sqrt((-1)^2-4(8)(-24)))/(2*8)`

`=1/16+-sqrt(769)/16`