Express this rational function as a partial fraction : (53-2s) / (2s^2+11s+5)

Question

Please show working so I can understand the process.

Answer 1

2s^2+11s+5=(5+s)(1+2s). Therefore,

 

(53-2s)/(2s^2+11s+5) =(53-2s)/((s+5)(2s+1)) = A/(s+5)+ B/(2s+1).

 

53-2s=A(2s+1)+B(s+5)=(2A+B)s+(A+5B)

 

From here it follows that

A+5B=53

2A+B=-2

Solve for A  and B: A=-7, B=12. Hence

(53+2s)/(2s^2+11s+5) = -7/(5+s)+ 12/(1+2s).