By using partial equation method, balance the equation :
`NaOH+Cl_(2)rarrNaCl+NaClO_(3)+H_(2)O`.

Explanation

(i) The probable partial equations for the above reaction are :
`{:(NaOH+Cl_(2)rarrNaCl+NaClO+H_(2)O....("equation 1")),(" "NaClOrarrNaClO_(3)+NaCl....("equation 2")):}`
(ii) After employing hit and trial method, the balanced partial equations may be written as :
`{:(2NaOH+Cl_(2)rarrNaCl+NaClO+H_(2)O......("equation 1")),(" "2NaClOrarrNaClO_(3)+NaCl......("equation 2")):}`
(iii) Multiply equation 1 by 3 in order to cancel out `NaClO` which does not appear in the final equation. Final equation. Finally add the two partial equations to get the final equation
`{:(" "2NaOH+Cl_(2)rarrNaCl+NaClO+H_(2)O"]"xx3......("equation 1")),(" "3NaClOrarrNaClO_(3)+2NaCl......("equation 2")),(bar(6NaOH+3Cl_(2)rarrNaClO_(3)+5NaCl+3H_(2)O)):}`.