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Question

Answer

$\frac{0.1 - i \cdot 0.5}{s - ( - 2 + i )} + \frac{0.1 + i \cdot 0.5}{s - ( - 2 - i )} = 0$

Explanation

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$\frac{0.1 - i \cdot 0.5}{s - ( - 2 + i )} + \frac{0.1 + i \cdot 0.5}{s - ( - 2 - i )} \frac{0.1 - 0 i}{s - ( - 2 + i )} + \frac{0.1 + 0 i}{s - ( - 2 - i )} \overset{◯}{1} \overset{◯}{2} \frac{0.1 - 0 i}{s + 2 - i} + \frac{0.1 + 0 i}{s + 2 + i} \overset{◯}{3} \frac{0}{- i ^{2} + s ^{2} + 4 s + 4} 0$
①	Remove the parentheses by changing the sign of each term within them. $- (- 2 + i) = 2 - i$
②	Remove the parentheses by changing the sign of each term within them. $- (- 2 - i) = 2 + i$
③	Add $\frac{00 i}{s + 2 - i}$ and $\frac{00 i}{s + 2 + i}$ to get $\frac{0}{- i ^{2} + s ^{2} + 4 s + 4}$ . To add raitonal expressions, both fractions must have the same denominator. We can create a common denominator by multiplying the first fraction by $i + s + 2$ and the second by $- i + s + 2$ . $\frac{00 i}{s + 2 - i} + \frac{00 i}{s + 2 + i} = \frac{( 00 i ) \cdot ( i + s + 2 )}{( s + 2 - i ) \cdot ( i + s + 2 )} + \frac{( 00 i ) \cdot ( - i + s + 2 )}{( s + 2 + i ) \cdot ( - i + s + 2 )} = = \frac{0 i 0 s 00 i ^{2} 0 i s 0 i}{i s + s ^{2} + 2 s + 2 i + 2 s + 4 - i ^{2} - i s - 2 i} + \frac{0 i 0 s 00 i ^{2} 0 i s 0 i}{i s + s ^{2} + 2 s + 2 i + 2 s + 4 - i ^{2} - i s - 2 i} = = \frac{0}{- i ^{2} + s ^{2} + 4 s + 4}$

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