Problem:
2​+3​+5​26​​ equals
Answer Choices:
A. 2​+3​−5​
B. 4−2​−3​
C. 2​+3​+6​−5
D. 21​(2​+5​−3​)
E. 31​(3​+5​−2​)
Solution:
Note that (2​+3​+5​)(2​+3​−5​)= (2​+3​)2−5=(5+26​)−5=26​. Thus
2​+3​+5​26​​=2​+3​+5​26​​⋅2​+3​−5​2​+3​−5​​=2​+3​−5​
Remark. In general, m​+n​+m+n​2mn​​=m​+n​−m+n​.