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I just started learning kanji so I might be missing something very basic.
剃刀 = 剃 + 刀
How come I can't combine 剃 and 刀's readings to form kamisori?
A word combined of two kanjis doesn't always read as those two kanjis combined. In fact, lots of time it doesn't.
This word, written as 剃刀, it is actually "髪(kami)剃り(sori)". Because this is a tool people use to shave their hair. It read as "shave" and "hair."