Question

Question #9c78e

Answer 1

`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:)