A three-body scattering process in the presence of Coulomb interaction can be decomposed formally into two-body single channel scattering, two-body multichannel scattering, and genuine three-body scattering. The corresponding integral equations are coupled Lippmann-Schwinger and Faddeev-Merkuriev integral equations. We solve these by applying the Coulomb-Sturmian separable expansion method. We present elastic scattering and reaction cross sections of the [Formula Presented] system both below and above the [Formula Presented] threshold. We find excellent agreements with previous calculations in most cases.