Question Number 144708 by mathdanisur last updated on 28/Jun/21
$${Simplify}:\:\:\left(\frac{\mathrm{1}}{\left({x}-\mathrm{2}\right)!}\:-\:\frac{\mathrm{1}}{\left({x}-\mathrm{1}\right)!}\right)\centerdot{x}! \\ $$
Answered by MJS_new last updated on 28/Jun/21
$$\left(\frac{\left({x}−\mathrm{1}\right){x}}{{x}!}−\frac{{x}}{{x}!}\right){x}!={x}^{\mathrm{2}} −\mathrm{2}{x}={x}\left({x}−\mathrm{2}\right) \\ $$
Commented by mathdanisur last updated on 28/Jun/21
$${cool}\:{thankyou}\:{Sir} \\ $$
Answered by liberty last updated on 28/Jun/21
$$\left(\frac{\mathrm{1}}{\left(\mathrm{x}−\mathrm{2}\right)!}−\frac{\mathrm{1}}{\left(\mathrm{x}−\mathrm{1}\right)\left(\mathrm{x}−\mathrm{2}\right)!}\right).\mathrm{x}\left(\mathrm{x}−\mathrm{1}\right)\left(\mathrm{x}−\mathrm{2}\right)! \\ $$$$=\left(\frac{\mathrm{x}−\mathrm{1}−\mathrm{1}}{\left(\mathrm{x}−\mathrm{1}\right)\left(\mathrm{x}−\mathrm{2}\right)!}\right).\mathrm{x}\left(\mathrm{x}−\mathrm{1}\right)\left(\mathrm{x}−\mathrm{2}\right)! \\ $$$$=\left(\frac{\mathrm{x}−\mathrm{2}}{\cancel{\left(\mathrm{x}−\mathrm{1}\right)\left(\mathrm{x}−\mathrm{2}\right)!}}\right).\mathrm{x}\cancel{\left(\mathrm{x}−\mathrm{1}\right)\left(\mathrm{x}−\mathrm{2}\right)!} \\ $$$$=\left(\mathrm{x}−\mathrm{2}\right).\mathrm{x}\: \\ $$
Commented by mathdanisur last updated on 28/Jun/21
$${thankyou}\:{Sir}\:{cool} \\ $$