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)✓](https://www.tinkutara.com/question/Q163342.png)
$$\frac{{a}^{\mathrm{2}} −{b}^{\mathrm{2}} }{{a}+{b}}={a}−{b} \\ $$$$=\left[\mathrm{1}+\frac{\mathrm{1}}{\mathrm{1}+\frac{\mathrm{1}}{\mathrm{100}}}−\left(\mathrm{1}−\frac{\mathrm{1}}{\mathrm{1}+\frac{\mathrm{1}}{\mathrm{100}}}\right)\right] \\ $$$$=\left[\mathrm{1}+\frac{\mathrm{1}}{\mathrm{1}+\frac{\mathrm{1}}{\mathrm{100}}}−\mathrm{1}+\frac{\mathrm{1}}{\mathrm{1}+\frac{\mathrm{1}}{\mathrm{100}}}\right] \\ $$$$\mathrm{2}\left(\frac{\mathrm{1}}{\mathrm{1}+\frac{\mathrm{1}}{\mathrm{100}}}\right)=\mathrm{2}×\frac{\mathrm{100}}{\mathrm{101}}=\frac{\mathrm{200}}{\mathrm{101}}\:\:\:\left({b}\right)\checkmark \\ $$