Using only p&p, determine the simplest fractional form of this expression:
3333373 - 3333263
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3333373 + 6666633
Note 333337 + 333326 = 666663. Then let A=333337 and B=333326. Then the fraction can be written as (A^3 - B^3) / (A^3 + (A+B)^3).
Factor the numerator and denominator
A^3 - B^3
= (A-B)*(A^2+AB+B^2)
A^3 + (A+B)^3
= (A+A+B)*(A^2-A*(A+B)+(A+B)^2)
= (2A+B)*(A^2+AB+B^2)
Then substitute these factorizations into (A^3 - B^3) / (A^3 + (A+B)^3)
= [(A-B)*(A^2+AB+B^2)] \ [(2A+B)*(A^2+AB+B^2)]
= (A-B)/(2A+B)
Last step is to resubstitute A=333337 and B=333326. Then (A-B)/(2A+B)
= (333337-333326)/(2*333337+333326)
= 11/1000000.
Another solution
