كتاب الصلاة
4  
The Book of Prayers
(11)
Chapter: It Is Obligatory To Recite Al-Fatihah In Every Rak'ah; If A Person Cannot Recite Al-Fatihah Or Cannot Learn It, Then He Should Recite Whatever Else He Can Manage
(11)
باب وُجُوبِ قِرَاءَةِ الْفَاتِحَةِ فِي كُلِّ رَكْعَةٍ وَإِنَّهُ إِذَا لَمْ يُحْسِنِ الْفَاتِحَةَ وَلاَ أَمْكَنَهُ تَعَلُّمُهَا قَرَأَ مَا تَيَسَّرَ لَهُ مِنْ غَيْرِهَا
Sahih Muslim 396 b

'Ata' narrated on the authority of Abu Huraira who said that one should recite (al-Fatiha) in every (rak'ah of) prayer. What we heard (i. e. recitation) from the Messenger of Allah (ﷺ), we made you listen to that. And that which he (recited) inwardly, we (recited) inwardly for you. A person said to him:

If I add nothing to the (recitation) of the Umm al Qur'an (Surat al-Fatiha), would it make the prayer incomplete? He (AbuHuraira) said: If you add to that (if you recite some of verses of the Qur'an along with Surat at-Fatiha) that is better for you. But if you are contented with it (Surat al-Fatiha) only, it is sufficient for you.
حَدَّثَنَا عَمْرٌو النَّاقِدُ، وَزُهَيْرُ بْنُ حَرْبٍ، - وَاللَّفْظُ لِعَمْرٍو - قَالاَ حَدَّثَنَا إِسْمَاعِيلُ بْنُ إِبْرَاهِيمَ، أَخْبَرَنَا ابْنُ جُرَيْجٍ، عَنْ عَطَاءٍ، قَالَ قَالَ أَبُو هُرَيْرَةَ فِي كُلِّ الصَّلاَةِ يَقْرَأُ فَمَا أَسْمَعَنَا رَسُولُ اللَّهِ صلى الله عليه وسلم أَسْمَعْنَاكُمْ وَمَا أَخْفَى مِنَّا أَخْفَيْنَا مِنْكُمْ ‏.‏ فَقَالَ لَهُ رَجُلٌ إِنْ لَمْ أَزِدْ عَلَى أُمِّ الْقُرْآنِ فَقَالَ إِنْ زِدْتَ عَلَيْهَا فَهُوَ خَيْرٌ وَإِنِ انْتَهَيْتَ إِلَيْهَا أَجْزَأَتْ عَنْكَ ‏.‏
Reference : Sahih Muslim 396b
In-book reference : Book 4, Hadith 45
USC-MSA web (English) reference : Book 4, Hadith 779
  (deprecated numbering scheme)