Question

Divide.,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,

Answer 1

It's not clear whether the problem is to:

(1) divide
`x^2-4` by
`(x-8)/(x-2)`, or

(2) divide
`(x^2-4)/(x-8)` by
`x-2`.

But with only two possible cases, that's not much work to do.


`\drac{x^2-4}{(x-8)/(x-2)}=((x^2-4)(x-2))/(x-8)=(x^3-2x^2-4x+8)/(x-8)`

Synthetic division yields a quotient and remainder of
`x^2+6x+44+(360)/(x-8)` (see attachment for how the algorithm was carried out).

In the other case,


`((x^2-4)/(x-2))/(x-8)=(((x-2)(x+2))/(x-2))/(x-8)=(x+2)/(x-8)`

provided that
`x\\eq2`. Synthetic division can be used again here, but this is quite easy to deal with by just doing some easy manipulation of the numerator:


`(x+2)/(x-8)=(x-8+10)/(x-8)=(x-8)/(x-8)+(10)/(x-8)=1+(10)/(x-8)`

(also provided that
`x\\eq 8`)