Solution of the Week #577 - Factorial Fun

46!/(45!+44!+43!)

 Write the denominator as:

43!*(45*44+44+1)

43!*(45*44+45)

43!*45*(44+1)

43!*45^2

Rewrite the numerator as:

46*45*44*43!

Putting the fraction back together and cancelling the 43! and one of the 45s:

46*44/45

Rewrite 46*44 as 45^2-1

 45^2/45 – 1/45

 45-1/45

44 44/45