3.5.2 (a! ± b!) / c!

This problem has pretty much nothing to do with factorials and mostly with basic fraction simplification. Take the following example:

8!+6!7!=8!7!+6!7!=817\frac{8! + 6!}{7!} = \frac{8!}{7!} + \frac{6!}{7!} = 8 \frac{1}{7}

Sometimes it is easier to just factor out the common factorial, for example:

3!+4!−5!3!=3!⋅(1+4−5⋅4)3!=1+4−20=−15\frac{3! + 4! - 5!}{3!} = \frac{3! \cdot (1 + 4 - 5 \cdot 4)}{3!} = 1 + 4 - 20 = -15

Problem Set 3.5.2

frac8!+6!7!=\\frac{8! + 6!}{7!} =
frac10!+8!9!=\\frac{10! + 8!}{9!} =
frac7!−5!6!=\\frac{7! - 5!}{6!} =
frac11!−9!10!=\\frac{11! - 9!}{10!} =
frac10!−11!9!=\\frac{10! - 11!}{9!} =
6cdot5cdot4!−5!=6 \\cdot 5 \\cdot 4! - 5! =
(2!+3!)div5!=(2! + 3!) \\div 5! =
(2!times3!)−4!=(2! \\times 3!) - 4! =
7!div6!−5!=7! \\div 6! - 5! =
7times5!−6!=7 \\times 5! - 6! =
2!−3!times5!=2! - 3! \\times 5! =
8!div6!−4!=8! \\div 6! - 4! =
frac5!cdot4!6!=\\frac{5! \\cdot 4!}{6!} =
frac4times5!−5times4!4!=\\frac{4 \\times 5! - 5 \\times 4!}{4!} =
frac4times5!+5times4!4!=\\frac{4 \\times 5! + 5 \\times 4!}{4!} =
frac6times7!−7times6!6!=\\frac{6 \\times 7! - 7 \\times 6!}{6!} =
frac10times9!−10!times99!=\\frac{10 \\times 9! - 10! \\times 9}{9!} =
frac8!times7−8times7!7!=\\frac{8! \\times 7 - 8 \\times 7!}{7!} =
frac11times10!−11!times1011!=\\frac{11 \\times 10! - 11! \\times 10}{11!} =
6!div(3!times2!)=6! \\div (3! \\times 2!) =