Home » » Express $$\cfrac{3s - 1}{(s + 1)(s - 3)}$$ as partial fractions

# Express $$\cfrac{3s - 1}{(s + 1)(s - 3)}$$ as partial fractions

### Question

Express $$\cfrac{3s - 1}{(s + 1)(s - 3)}$$ as partial fractions

### Options

A) $$\frac{1}{(s+1)}+\frac{2}{(s-3)}$$

B) $$\frac{2}{(s+1)}-\frac{1}{(s-3)}$$

C) $$\frac{2}{(s+3)}+\frac{1}{(s-1)}$$

D) $$\frac{1}{(s-1)}+\frac{2}{(s-3)}$$

### Explanation:

3s-1\(s+1)(s-3)=A/(s+1)+B/(s-3)
3s-1\{s+1)(s-3)=A(s-3)+B(s+1)
3s-1/(s+1)(s-3)=A(s-3)+B(s+1)/(s+1)(s-3)
denominator cancels each other
3s-1=A(s-3)+B(s+1)
If s=+3
3(3)-1=A(3-3)+B(3+1)
[A(0)=0]
9-1=4B
8=4B
B=8/4
B=2✓
If s=-1
3s-1=A(s-3)+B(s+1)
3(-1)-1=A(-1-3)+B(-1+1)
-4=-4A
A=-4/-4
A=1✓

Explanation provided by Franklin Precious

## Discussion (2)

• Do trial and error...the one that gives you back the question is the answer

• 3s-1\(s+1)(s-3)=A/(s+1)+B/(s-3)
3s-1\{s+1)(s-3)=A(s-3)+B(s+1)
3s-1/(s+1)(s-3)=A(s-3)+B(s+1)/(s+1)(s-3)
denominator cancels each other
3s-1=A(s-3)+B(s+1)
If s=+3
3(3)-1=A(3-3)+B(3+1)
[A(0)=0]
9-1=4B
8=4B
B=8/4
B=2✓
If s=-1
3s-1=A(s-3)+B(s+1)
3(-1)-1=A(-1-3)+B(-1+1)
-4=-4A
A=-4/-4
A=1✓