What is expand ,(1/(44+210j)+1/(50+80j)) ?

The solution to expand ,(1/(44+210j)+1/(50+80j)) is (145j+47)/(8400j^2+7010j+1100)

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expand ,(1/(44+210j)+1/(50+80j))

expand

\frac{1}{44 + 210 j} + \frac{1}{50 + 80 j}

\frac{145 j + 47}{8400 j ^{2} + 7010 j + 1100}

Solution steps

\frac{1}{44 + 210 j} + \frac{1}{50 + 80 j}

Factor

44 + 210 j : 2 (105 j + 22)

= \frac{1}{2 ( 105 j + 22 )} + \frac{1}{50 + 80 j}

Factor

50 + 80 j : 10 (8 j + 5)

= \frac{1}{2 ( 105 j + 22 )} + \frac{1}{10 ( 8 j + 5 )}

Least Common Multiplier of

2 (105 j + 22), 10 (8 j + 5) : 10 (8 j + 5) (105 j + 22)

Adjust Fractions based on the LCM

= \frac{5 ( 8 j + 5 )}{10 ( 8 j + 5 ) ( 105 j + 22 )} + \frac{105 j + 22}{10 ( 8 j + 5 ) ( 105 j + 22 )}

Since the denominators are equal, combine the fractions:

\frac{a}{c} \pm \frac{b}{c} = \frac{a \pm b}{c}

= \frac{5 ( 8 j + 5 ) + 105 j + 22}{10 ( 8 j + 5 ) ( 105 j + 22 )}

Expand

10 (8 j + 5) (105 j + 22) : 8400 j^{2} + 7010 j + 1100

= \frac{5 ( 8 j + 5 ) + 105 j + 22}{8400 j ^{2} + 7010 j + 1100}

Expand

5 (8 j + 5) + 105 j + 22 : 145 j + 47

= \frac{145 j + 47}{8400 j ^{2} + 7010 j + 1100}

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What is expand ,(1/(44+210j)+1/(50+80j)) ?
The solution to expand ,(1/(44+210j)+1/(50+80j)) is (145j+47)/(8400j^2+7010j+1100)