Partial fraction

[Adhamhashem2022]

I need to solve this partial fraction please e^x/((x-i)(x+i))
The result will be ( (e^x*i) / 2(x+i) )
) - ( (e^x*i) / 2(x-i) )
but I don't know how to get this result!!

 

[topsquark]

I need to solve this partial fraction please e^x/((x-i)(x+i))
The result will be ( (e^x*i) / 2(x+i) )
) - ( (e^x*i) / 2(x-i) )
but I don't know how to get this result!!

It's a good thing that you don't know how to get that result because it's wrong!

[imath]\dfrac{e^{x}}{(x + i)(x - i)} = e^x \left ( \dfrac{1}{(x + i)(x - i)} \right ) = e^x \left ( \dfrac{A}{x + i} + \dfrac{B}{x - i} \right )[/imath]

How do you get A and B?

-Dan

 

[Adhamhashem2022]

It's a good thing that you don't know how to get that result because it's wrong!

[imath]\dfrac{e^{x}}{(x + i)(x - i)} = e^x \left ( \dfrac{1}{(x + i)(x - i)} \right ) = e^x \left ( \dfrac{A}{x + i} + \dfrac{B}{x - i} \right )[/imath]

How do you get A and B?

-Dan

I understand what you said but I need to do this to solve this problem

 

[Adhamhashem2022]

This is The full answer to this problem which we use The partial fraction to solve it, i do not understand how he solved the partial fraction.

 

[AvgStudent]

This is The full answer to this problem which we use The partial fraction to solve it, i do not understand how he solved the partial fraction.

Hi @Adhamhashem2022,
\(\displaystyle \dfrac{1}{(x-i)(1+i)}=\dfrac{A}{x-i}+\dfrac{B}{x+i}= \dfrac{A(x+i)+B(x-i)}{(x-i)(x+i)}\)

Compare the numerator.
\(\displaystyle 1=A(x+i)+B(x-i)\)

The next step would be to multiply out the right-hand side, collect the common terms and then equate the coefficient.

Hopes this help