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