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Question Number 163340 by mathlove last updated on 06/Jan/22

Answered by Rasheed.Sindhi last updated on 06/Jan/22

((a^2 −b^2 )/(a+b))=a−b  =[1+(1/(1+(1/(100))))−(1−(1/(1+(1/(100)))))]  =[1+(1/(1+(1/(100))))−1+(1/(1+(1/(100))))]  2((1/(1+(1/(100)))))=2×((100)/(101))=((200)/(101))   (b)✓

$$\frac{{a}^{\mathrm{2}} −{b}^{\mathrm{2}} }{{a}+{b}}={a}−{b} \\ $$$$=\left[\mathrm{1}+\frac{\mathrm{1}}{\mathrm{1}+\frac{\mathrm{1}}{\mathrm{100}}}−\left(\mathrm{1}−\frac{\mathrm{1}}{\mathrm{1}+\frac{\mathrm{1}}{\mathrm{100}}}\right)\right] \\ $$$$=\left[\mathrm{1}+\frac{\mathrm{1}}{\mathrm{1}+\frac{\mathrm{1}}{\mathrm{100}}}−\mathrm{1}+\frac{\mathrm{1}}{\mathrm{1}+\frac{\mathrm{1}}{\mathrm{100}}}\right] \\ $$$$\mathrm{2}\left(\frac{\mathrm{1}}{\mathrm{1}+\frac{\mathrm{1}}{\mathrm{100}}}\right)=\mathrm{2}×\frac{\mathrm{100}}{\mathrm{101}}=\frac{\mathrm{200}}{\mathrm{101}}\:\:\:\left({b}\right)\checkmark \\ $$

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