reserve a,b,c,x,y,z for Real;

theorem Th10:
  for a, b being Complex st a^2 - b^2 <> 0 holds
    1/(a+b) = (a-b)/(a^2-b^2)
proof
  let a, b be Complex;
  assume a^2-b^2 <> 0;
  then (a-b) <> 0;
  hence 1/(a+b) = (1*(a-b))/((a+b)*(a-b)) by XCMPLX_1:91
    .= (a-b)/(a^2-b^2);
end;
