Proof t is irrational t = a-bs ,Given a and b are rational numbers, b $\neq 0$ and s is irrational. 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.
