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Question Number 144708 by mathdanisur last updated on 28/Jun/21

Simplify:  ((1/((x-2)!)) - (1/((x-1)!)))∙x!

$${Simplify}:\:\:\left(\frac{\mathrm{1}}{\left({x}-\mathrm{2}\right)!}\:-\:\frac{\mathrm{1}}{\left({x}-\mathrm{1}\right)!}\right)\centerdot{x}! \\ $$

Answered by MJS_new last updated on 28/Jun/21

((((x−1)x)/(x!))−(x/(x!)))x!=x^2 −2x=x(x−2)

$$\left(\frac{\left({x}−\mathrm{1}\right){x}}{{x}!}−\frac{{x}}{{x}!}\right){x}!={x}^{\mathrm{2}} −\mathrm{2}{x}={x}\left({x}−\mathrm{2}\right) \\ $$

Commented by mathdanisur last updated on 28/Jun/21

cool thankyou Sir

$${cool}\:{thankyou}\:{Sir} \\ $$

Answered by liberty last updated on 28/Jun/21

((1/((x−2)!))−(1/((x−1)(x−2)!))).x(x−1)(x−2)!  =(((x−1−1)/((x−1)(x−2)!))).x(x−1)(x−2)!  =(((x−2)/((x−1)(x−2)!))).x(x−1)(x−2)!  =(x−2).x

$$\left(\frac{\mathrm{1}}{\left(\mathrm{x}−\mathrm{2}\right)!}−\frac{\mathrm{1}}{\left(\mathrm{x}−\mathrm{1}\right)\left(\mathrm{x}−\mathrm{2}\right)!}\right).\mathrm{x}\left(\mathrm{x}−\mathrm{1}\right)\left(\mathrm{x}−\mathrm{2}\right)! \\ $$$$=\left(\frac{\mathrm{x}−\mathrm{1}−\mathrm{1}}{\left(\mathrm{x}−\mathrm{1}\right)\left(\mathrm{x}−\mathrm{2}\right)!}\right).\mathrm{x}\left(\mathrm{x}−\mathrm{1}\right)\left(\mathrm{x}−\mathrm{2}\right)! \\ $$$$=\left(\frac{\mathrm{x}−\mathrm{2}}{\cancel{\left(\mathrm{x}−\mathrm{1}\right)\left(\mathrm{x}−\mathrm{2}\right)!}}\right).\mathrm{x}\cancel{\left(\mathrm{x}−\mathrm{1}\right)\left(\mathrm{x}−\mathrm{2}\right)!} \\ $$$$=\left(\mathrm{x}−\mathrm{2}\right).\mathrm{x}\: \\ $$

Commented by mathdanisur last updated on 28/Jun/21

thankyou Sir cool

$${thankyou}\:{Sir}\:{cool} \\ $$

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