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