Proof $t$ is irrational $ t = a-bs $ , Given $a$ and $b$ are rational numbers, $b \neq 0$ and $s$ is irrational. Hence show that $(\sqrt3-1)/(\sqrt3+1)$ is irrational
For the first part: in a comment you have solved for $s$ in terms of $a$, $b$ and $t$. You know the first two are rational. What could you say about $s$ if $t$ were rational too?
You have started the second part correctly. Now it's in a form where you can apply the first part.
For the first part
$a/b -s = t/b$
Assuming t was rational would mean $ s $ is rational since rational numbers are closed under addition and subtraction.
This contradicts s being irrational. Therefore t is irrational.
The second part $(\surd3-1)/(\surd3+1) * (\surd3-1)/(\surd3-1) $
Therefore $t=2-\surd3$ is irrational too.