Question #9c78e

1 Answer
Oct 16, 2017

a=1,b=7,c=-3.

Explanation:

Given,

f(x)=x+a+b/(x+1)+c/(x+1)^2

Now find out the LCM and add up all the terms.

f(x)=(x(x+1)^2+a(x+1)^2+b(x+1)+c)/(x+1)^2

:.color(red)(f(x)=(x^3+(a+2)x^2+(2a+b+1)x+(a+b+c))/(x+1)^2).......(1).

Again given that,

color(red)(f(x)=(x^3+3x^2+10x+5)/(x+1)^2).......(2).

Now, comparing the coefficients of these two equations we get three more equations rarr

a+2=3........(a).

2a+b+1=10........(b).

a+b+c=5........(c).

Now solving these three equations we get,

color(red)(a=1,b=7,c=-3). (Answer).

Hope if Helps:)