Maths question about ratio

a :b = x : y
Let a = xk, where k is a constant.
Then, b = yk

L.S.
= (pa² + qax + rx²) : (pb² + qby + ry²)
= [p(xk)² + q(xk)x + rx²] : [p(yk)² + q(yk)y + ry²]
= (px²k² + qx²k + rx²) : (py²k² + qy²k + ry²)
= x²(pk² + qk + r) : y²(pk² + qk + r)
= x² : y²
= x²(k² + 1) : y²(k² + 1)
= (x²k² + x²) : (y²k² + y²)
= [(xk)² + x²] : [(yk)² + y²]
= (a² + x²) : (b² + y²)
= R.S.

Hence, (pa² + qax + rx²) : (pb² + qby + ry²) = (a² + x²) : (b²+ y²)

自稱 Teacher，回答採用率 0/18，行開啲啦。