Question

If $\frac{1}{8!}+\frac{1}{9!}=\frac{x}{10!},$ find $x.$

Answer 1

Simplification,
$\frac{1}{8!}+\frac{1}{9!}=\frac{x}{10!}$
$\Rightarrow 10![\frac{1}{8!}+\frac{1}{9!}]=x$
$\Rightarrow \frac{10!}{8!}+\frac{10!}{9!}=x$
$\Rightarrow \frac{10\times 9\times 8!}{8!}+\frac{10\times 9!}{9!}=x$
$\Rightarrow 90+10=x$
$\therefore x=100$