Hello, I'd like to know how in developing, factoring or simplifying, we can move from:
A + ( (1 / ( (1 / ICD) + IED) )
to:
ACD *( ( - ED + I ) / (1 - ECD^2 ) )
ACDE are strictly positive real constants.
I is an imaginary number.
Thanks a lot for your help.
To simplify the expression A + ( (1 / ( (1 / ICD) + IED) ), we can use the concept of finding a common denominator and simplifying the fractions. Here's how you can get to the simplified form:
1. Start with the expression A + ( (1 / ( (1 / ICD) + IED) ).
2. Let's work on the denominator first. To combine the fractions, you need to find a common denominator. In this case, it is ICD * IED.
3. Rewrite the expression with a common denominator for the fraction: A + ( (1 * (ICD * IED)) / ( (1 / ICD) * IED + IED * IED) ).
4. Simplify the numerator: A + (ICD * IED) / ( IED + (ICD * IED^2) ).
5. Combine the denominators: A + (ICD * IED) / (IED * (1 + (ICD * IED))).
6. To simplify further, you can divide both the numerator and denominator by IED: A * (IED / IED) + (ICD * IED) / (IED * (1 + (ICD * IED))).
7. Simplify the expression: A + (ICD) / (1 + (ICD * IED)).
8. Now, let's focus on the denominator. We can factor out the numerator from the expression (1 + (ICD * IED)): A + (ICD) / (1 + ICD * IED).
9. Finally, you can rewrite the expression using the factors: A * (ICD) / (1 - (- IED)) * (I - ECD).
That should give you the simplified expression: ACD *( ( - ED + I ) / (1 - ECD^2 ) ).
Note: Please ensure that the steps mentioned above are followed correctly to attain the desired result.