Five Hindrances Right Mindfulness Interrelated? Dear Buddhist Community, 

Would someone help to explain how eradicating/suppressing the five hindrances and right mindfulness can go together?

According to the Buddha: (http://what-buddha-said.net/drops/II/Feeding_the_Hindrances.htm)


  "Just as this body, is sustained by food, is dependent on food, and
  cannot  continue without food, even so, friends, are the five mental
  hindrances  indeed also sustained by a kind of food, they are also
  dependent on food,  and cannot continue without ever renewed feeding!
  
  And what, friends, is feeding for the arising and growth of
  sense-desire?  It is frequent and careless attention to the alluring
  and attractive features! This food makes sensual lust arise, and feeds
  also growth of habitual greed…
  
  And what, friends, is feeding for the arising and aggravation of
  ill-will?  It is frequent and careless attention to the displeasing
  and repulsive features! This food makes aversion arise, and boosts
  also any habitual irritation…
  
  And what feeds the emergence and deterioration of
  lethargy-and-laziness?  It is frequent and careless attention to
  drowsiness, and too much  eaten  dullness! This is feeding makes sloth
  arise, and feeds also worsening of habitual laziness…
  
  And what feeds the arising and escalation of restlessness-and-regret? 
  It is frequent and careless attention to the excited, agitated, and
  stressed up mind! This food upsets and stirs the mind, and intensifies
  also habitual anxiety and worry…
  
  And what feeds the arising, deepening, and  expansion of 
  doubt-and-uncertainty? It is frequent and careless attention to
  doubtful theories and speculative views! This food bewilders the mind,
  and feeds also the escalation of habitual confusion..."


Notice, the key phrase the Buddha used is: IT IS THE FREQUENCT AND CARELESS ATTENTION to the hindrances listed above. So, are we supposed to be simply ignoring these thoughts of hindrance as they arise? 

Or, more generally, would someone explain how hindrances and right mindfulness go together? 

I know that it might be a silly question, but this question has bugged me for some time now. 

Thank you for your help everyone! 
Reid
The Pāḷi phrase for "frequent and careless attention in the Sutta (SN 46.2) is "ayonisomanasikārabahulīkāro". 

ayoniso = unwise, manasikāra = attention, bahulīkāro = continuous practice

The role of manasikāra is to direct the mind, just as a rudder steers a boat. Manasikāra can be wholesome or unwholesome. 

When manasikāra is steering the mind in a way that is in concordance with the dhamma, this is called "wise attention" (yonisomanasikāra). Wise attention is a proximate cause for non-attachment (alobha), non-aversion (adosa), equanimity (tatramajjhattatā) and understanding (paññā).

When manasikāra is steering the mind in a way that is not in concordance with the dhamma, this is called "unwise attention" (ayonisomanasikāra). Unwise attention is a proximate cause for delusion (moha), restlessness (uddhacca) and doubt (vicikicchā).

Accoding to Iti 1.16:


  This was said by the Blessed One, said by the Arahant, so I have heard: "With regard to internal factors, I don't envision any other single factor like wise attention as doing so much for a monk in training, who has not attained the heart's goal but remains intent on the unsurpassed safety from bondage. A monk who attends appropriately abandons what is unskillful and develops what is skillful.