Putting prayers together because of being too busy with breastfeeding
Question

                My son is 7 weeks old and I am breastfeeding. I wanted to ask can I recite the Holy quran while feeding him because at times he is feeding very frequently and I cant make separate time for reciting.

Also can I combine prayers as the baby at times demands alot of attention because of which I can't pray on times.only once in a while I can!

Your advice and guidance is highly appreciated.
Praise be to Allah.
      Firstly: 

    It is permissible for the breastfeeding mother to recite 
    Qur’aan whilst breastfeeding her infant, and there is nothing wrong with it, 
    even if she reads from the Mushaf, so long as she has wudoo’. Otherwise she 
    should hold it with a barrier such as gloves and the like. See the answer to 
    question no. 10672 and
    8950. 

    Secondly: 

    What is required is to offer the prayers at the proper times 
    as enjoined by Allah. Allah, may He be glorified, says (interpretation of 
    the meaning):

    “Verily, As‑Salaah (the prayer) is enjoined on the 
    believers at fixed hours”

    [al-Nisa’ 4:103]

    i.e., they are obligatory and must be offered at specific 
    times. 

    It is not permissible to put two prayers together except for 
    a reason such as travelling, rain or sickness. 

    Ibn Abi Shaybah (2/346) narrated that Abu Moosa al-Ash‘ari 
    and ‘Umar ibn al-Khattaab (may Allah be pleased with them both) said: 
    “Putting two prayers together without an excuse is a major sin.” 

    Some of the scholars said that one of the excuses that make 
    it permissible to put two prayers together is: “… for the breastfeeding 
    woman because of the difficulty caused by there being a great deal of 
    najaasah (impurities)” -- i.e., because it is difficult for her to purify 
    herself for every prayer. Abu’l-Ma‘aali said: She is like one who is sick.

    End quote from Kashshaaf al-Qinaa‘, 2/5. 

    i.e., if there is some impurity (najaasah) that gets onto her 
    from her infant, and it is too difficult for her to purify herself or change 
    or wash her clothes, then it is permissible for her to put prayers together. 
     

    But if she does not get any najaasah on her, especially 
    nowadays with the availability of diapers (nappies) that keep the najaasah 
    from spreading, it does not seem that there are any excuses. Doing wudoo’ 
    and praying takes only ten minutes or a little more, so it does not make 
    sense that a woman could be distracted with her infant to such an extent 
    that she cannot leave him for this short period of time. She should take 
    advantage of his naptime or times when he is calm to offer her prayer in the 
    best and most complete manner. 

    Prayer is the greatest act of worship and the most important 
    pillar of Islam after the twin declaration of faith (Shahaadatayn). The 
    Muslim is enjoined to pray regularly and to pay attention to the matter of 
    prayer and give it its proper measure, because it is the connection between 
    him and his Lord; if he neglects it there is no greater loss than that. 

    So our advice to you is to pay attention to your prayer and 
    offer prayers regularly on time; remember that this is one of the means of 
    barakah (blessing), protection and divine support, as Allah, may He be 
    exalted, says (interpretation of the meaning): 

    “Whoever works righteousness — whether male or female — 
    while he (or she) is a true believer (of Islamic Monotheism) verily, to him 
    We will give a good life (in this world with respect, contentment and lawful 
    provision), and We shall pay them certainly a reward in proportion to the 
    best of what they used to do (i.e. Paradise in the Hereafter)”

    [al-Nahl 16:97] 

    “And whosoever fears Allaah and keeps his duty to Him, He 
    will make a way for him to get out (from every difficulty).

    3. And He will provide him from (sources) he never could 
    imagine. And whosoever puts his trust in Allaah, then He will suffice him. 
    Verily, Allaah will accomplish his purpose. Indeed Allaah has set a measure 
    for all things”

    [al-Talaaq 65:2-3]. 

    And Allah knows best.