Ruling on one who prays on a carpet, the edges of which reach the bathroom
Question

                If a person prays in a bedroom which has a fitted carpet that reaches the threshold of the bathroom, and he thinks that the edge of the carpet that is nearest to the bathroom is najis (impure) because people step on it after they come out of the bathroom, and that some impurities such as urine and the like may get on it, but he prays on his own prayer mat, is his prayer valid? And is it okay to pray in this room?
Praise be to Allah.
    
    Firstly: 

    In 
    order for prayer to be valid, it is stipulated that the person’s clothes and 
    body, and the place where he prays, should be pure and clean. If a person 
    knowingly prays on unclean ground, or in an unclean garment, or with an 
    unclean substance on his body, then his prayer is not valid. Allah, may He 
    be exalted, says (interpretation of the meaning): “And 
    your garments purify!” 
    [al-Muddaththir 74:4]

    It was 
    narrated from Asma bint Abi Bakr as-Siddeeq that she said: A woman asked the 
    Messenger of Allah (blessings and peace of Allah be upon him): O Messenger 
    of Allah, what do you think if menstrual blood gets on the garment of one of 
    us, what should she do? The Messenger of Allah (blessings and peace of Allah 
    be upon him) said: “If menstrual blood gets on the garment of one of you, 
    let her scratch it off and sprinkle it with water, then let her pray in it.”
    

    
    Narrated by al-Bukhaari (307) and Muslim (291). 

    Ibn 
    ‘Abd al-Barr (may Allah have mercy on him) said: This hadeeth is the main 
    guideline on washing the impurities from clothes.

    End 
    quote from al-Istidhkaar, 1/291 

    
    An-Nawawi (may Allah have mercy on him) said: Our view is that removing 
    impurities is a condition of prayer being valid, whether it is an obligatory 
    or supererogatory (naafil) prayer, or a funeral prayer, or the prostration 
    of recitation, or the prostration of thankfulness. Removal of impurities is 
    stipulated in all cases. This is our view and it is also the view of Abu 
    Haneefah, Ahmad and all the scholars of the earlier and later generations. 

    Three 
    reports were narrated from Maalik about removing impurities, the soundest 
    and most well known of which is that if a person prays knowing that some 
    impurity is present, his prayer is not valid, but if he was not aware of it 
    or he forgot, then it is valid. This is an older view narrated from 
    ash-Shaafa‘i, and his later view is that the prayer is not valid, whether he 
    was aware of it or not, or he forgot.

    End 
    quote from al-Majmoo‘, 3/139 

    Shaykh 
    ‘Abdullah ibn Saalih al-Fawzaan (may Allah preserve him) said: This 
    indicates that one should not pray in an unclean garment; rather one should 
    pray in a clean and pure garment. This is among the strongest evidence that 
    it is obligatory to purify one’s garments for prayer.

    End 
    quote from Minhah al-‘Allaam Sharh Buloogh al-Maraam (1/1808) 

    
    Secondly: 

    If a 
    person prays on a carpet, the edge of which is impure or in contact with 
    something impure, or it is spread over something that is impure, his prayer 
    is still valid, because he is not in direct contact with the impurity. 

    Ibn 
    Qudaamah (may Allah have mercy on him) said: If he prays on a cloth, the 
    edge of which is impure, or if there is beneath his feet of rope that is 
    tied to something impure, but what he is praying on is pure, then his prayer 
    is valid, regardless of whether or not the impurity moves when he moves. 
    That is because he is not carrying the impurity and is not praying on it; 
    rather his prayer mat is in contact with it. This is like if he prays on 
    pure ground that is connected to impure ground.

    End 
    quote from al-Mughni (402). 

    
    An-Nawawi (may Allah have mercy on him) said: If there is any impurity on 
    the carpet or mat and the like, and he prays on the spot where the impurity 
    is, then his prayer is not valid, but if he prays on a clean spot of the 
    mat, then his prayer is valid. Our companions said: (This applies) 
    regardless of whether or not the carpet moves when he moves, because he is 
    not carrying or touching the impurity. The same applies if he prays on a bed 
    the feet of which are standing on something impure; his prayer is valid, 
    even if it moves when he moves.

    End 
    quote from al-Majmoo‘ (3/159). 

    Based 
    on the above, if a person prays in a room in which there is something 
    impure, or he prays on the carpet, the edge of which is impure, or that is 
    spread over something impure, but he does not have any direct contact with 
    the impurity, then his prayer is valid. 

    Note: 

    Places 
    where people pray or other places cannot be ruled to be impure unless it is 
    known that impurity has indeed gotten onto them. The fact that people walk 
    on the carpet after they come out of the washroom does not necessarily imply 
    that the carpet has become impure. The basic principle is that this place is 
    definitely pure and that there is some doubt concerning impurity. One of the 
    ways in which Islam makes things easy for people is that the basic principle 
    that a thing is definitely pure remains in effect and we do not rule that a 
    place is impure unless it is known that it has indeed become impure. 

    And 
    Allah knows best.