What is (5!7!)/(3!9!) ?

The solution to (5!7!)/(3!9!) is 5/18

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simplify (5!7!)/(3!9!)

simplify

\frac{5 ! 7 !}{3 ! 9 !}

\frac{5}{18}

Decimal Notation

0.27777 \dots

Solution steps

\frac{5 ! \cdot 7 !}{3 ! \cdot 9 !}

Cancel the factorials:

\frac{n !}{( n - m ) !} = n \cdot (n - 1) \dots (n - m + 1), n > m

\frac{5 !}{3 !} = 5 \cdot 4

= \frac{5 \cdot 4 \cdot 7 !}{9 !}

Cancel the factorials:

\frac{n !}{( n + m ) !} = \frac{1}{( n + 1 ) \cdot ( n + 2 ) \dots ( n + m )}

\frac{7 !}{9 !} = \frac{1}{8 \cdot 9}

= \frac{5 \cdot 4}{8 \cdot 9}

Cancel

\frac{5 \cdot 4}{8 \cdot 9} : \frac{5}{2 \cdot 9}

= \frac{5}{2 \cdot 9}

Multiply the numbers:

2 \cdot 9 = 18

= \frac{5}{18}

- x^{2} + 4 x + 5

2 x^{2} + 15 x = 8 x - 5

\frac{8}{3} - 8

2 (- 2) - 1

216