Question

Simplifique as expressões:

a)
$\frac{10!}{7! + 5!}$
b)
$\frac{9! - 7!}{6!}$
​

Answer 1

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$\tt a)~\sf\dfrac{10!}{7!+5!}=\dfrac{10\cdot9\cdot8\cdot7\cdot6\cdot5!}{7\cdot6\cdot5!+5!}\\\sf=\dfrac{10\cdot9\cdot8\cdot7\cdot6\cdot5!}{5!(42+1)}=\dfrac{10\cdot9\cdot8\cdot7\cdot6\cdot\diagup\!\!\!\!\!5!}{43\cdot\diagup\!\!\!\!\!5!}=\dfrac{30240}{43}$

$\tt b)~\sf\dfrac{9!-7!}{6!}=\dfrac{9\cdot8\cdot7\cdot6!-7\cdot6!}{6!}\\\sf=\dfrac{\diagup\!\!\!\!\!6!(504-7)}{\diagup\!\!\!\!\!6!}=497$