- #1

ChiralSuperfields

- 1,316

- 141

- Homework Statement
- Please see below

- Relevant Equations
- ##\frac{2s + 1}{((s - 1)(s - 1)} = \frac{A(s - 1) + B(s - 1)}{(s - 1)(s - 1)}##

For this problem (b),

The solution is,

However, I don't understand how they got their partial fractions here (Going from step 1 to 2).

My attempt to convert into partial fractions is:

##\frac{2s + 1}{(s - 1)(s - 1)} = \frac{A(s - 1) + B(s - 1)}{(s - 1)(s - 1)}##

Thus,

##2s + 1 = A(s - 1) + B(s - 1)##

##2s + 1 = (A + B)s - A - B##

##2 = A + B##

##1 = - A - B##

##-1 = A + B##

However, ##2 ≠ -1##

Does someone please know how they got their partial fractions expression in step 2?

Thanks!

The solution is,

However, I don't understand how they got their partial fractions here (Going from step 1 to 2).

My attempt to convert into partial fractions is:

##\frac{2s + 1}{(s - 1)(s - 1)} = \frac{A(s - 1) + B(s - 1)}{(s - 1)(s - 1)}##

Thus,

##2s + 1 = A(s - 1) + B(s - 1)##

##2s + 1 = (A + B)s - A - B##

##2 = A + B##

##1 = - A - B##

##-1 = A + B##

However, ##2 ≠ -1##

Does someone please know how they got their partial fractions expression in step 2?

Thanks!