Question

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

Answer 1

On multiplying both sides by $10!$, we get

$x=\frac{10!}{8!}+\frac{10!}{9!}\Rightarrow x=\frac{10\times 9\times (8!)}{(8!)}+\frac{10\times (9!)}{(9!)}$

$\Rightarrow x=(10\times 9)+10=(90+10)=100.$

Hence, $x=100.$