You'd need to solve for the positive value k first.
$\displaystyle \frac{1}{k-1}=3+\frac{1}{k}=\frac{3k+1}{k}$
Use the k obtained and substitute it into the x equation to find x.
The k equation will end up as a quadratic to solve as before.
Then just put the value you get for k into the x equation to find x.
The two sets of brackets show you how to find k.
Remember the song by Desmond Decker ? (No, you're probably too young)
"You can get it if you really want, but you must try, try and try, try and try, you'll succeed at last".
I had the correct value for b but I forgot the plus/minus. I divided that polynomial by 3. It helps keep it simpler for me personally. If I stray into too much algebra I will surely stumble somewhere :P
k^2-k-1/3 a=1 b=-1 c=-1/3
k=[1+√(1+4/3)]/2 correct?
I also added the fraction wrong LOL
It should work out to [1+√(7/3)]/2 correct?
Now I solved for the repeating part in #4. Do I do anything with the rest of that where you said you relate x to k or whatever. Or do i just state that?
Your equation to find x contains a k, so you substitute in that k value to find x.
If you could not find k, you cannot write the value of x.
But you should know this from algebraic substitution.
At this time, you should probably review solving algebraic equations in 2 unknowns.
It was not necessary to introduce k, but solving for x alone without introducing something like "k"
could be even messier.