If A +1/A = -1, then find the value of (A^6+A^3-1)/(A^9+A^3-1)

If $ A +\frac{1}{A} = -1$

Find the value of $\frac{A^6+A^3-1}{A^9+A^3-1}$

If $ A +\frac{1}{A} = -1$

Then, A³ = 1 always

Now put the value of A³ in $\frac{A^6+A^3-1}{A^9+A^3-1}$ = $\frac{1^2+1-1}{1^3+1^3-1}$ = 1