When you are doing problems like this, watch the denominators on the fractions --- you can't add or subtract thirds and fifths...you need the same denominator first which you can get by multiplying the two numbers (sometimes there is a smaller least common multiple.)
So here, if 1/3 are science, that is 5/15 science.
If 2/5 are biography, that is 6/15 biography.
The total number of books is 15/15, another way to write 1.
So if the rest are fiction, that would be 15/15 - 5/15 - 6/15 =