Question

How do you solve for x: `2/(x-3) - 3/(x+3) = 12/((x^2)-9)`?

Answer 1

`2/(x-3)-3/(x+3)=12/(x^2-9)`

`implies (2(x+3)-3(x-3))/((x+3)(x-3))=12/(x^2-9)`

`implies (2x+6-3x+9)/cancel(x^2-9)=12/cancel(x^2-9)`

`implies -x+15=12`

`implies x=3`

Verification: Put `x=3`

`L.H.S=2/(x-3)-3/(x+3)=2/(3-3)-3/(3+3)=2/0-3/6`

Here we can see `2/0`, in Mathematics, division by 0 is not allowed.
Hence, the root `x=3` is not a solution to the given equation.
Hence, no solution exists for the given equation.