If 1 6! + 1 7! = x 8! find x. - Vidyadip

Question

If $\frac{1}{{6!}} + \frac{1}{{7!}} = \frac{x}{{8!}}$ find x.

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Answer

Here
$\frac{1}{{6!}} + \frac{1}{{7!}} = \frac{x}{{8!}}$
$\Rightarrow \frac{1}{{6!}} + \frac{1}{{7 \times 6!}} = \frac{x}{{8 \times 7 \times 6!}}$
$ \Rightarrow \frac{1}{{6!}}\left[ {1 + \frac{1}{7}} \right] = \frac{1}{{6!}}\left[ {\frac{x}{{8 \times 7}}} \right]$
$\Rightarrow(1+\frac{1}{7})=\frac{x}{56}$
$\Rightarrow\frac{8}{7}=\frac{x}{56}$
$\Rightarrow8=\frac{x}{8}$
$\Rightarrow$ x = 64

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