We show that for an algebraic Riccati equation $X^*B^{-1}X-T^*X-X^*T=C$, its solutions are given by X = W + BT for some solution W of $X^*B^{-1}X$ = $C+T^*BT$. To generalize this, we give an equivalent condition for $(array{B&W\W*&A});{geq};0$ for given positive operators B and A, by which it can be regarded as Riccati inequality $X^*B^{-1}X{leq}A$. As an application, the harmonic mean B ! C is explicitly written even if B and C are noninvertible.