`(5-x)/(2x^2+x-1)`

`=(5-x)/(2x^2+2x-x-1)`

`=(5-x)/((2x(x+1)-1(x+1)))`

`=(5-x)/((2x-1)(x+1))`

Let `(5-x)/(2x^2+x-1)=A/(2x-1)+B/(x+1)`

`(5-x)/(2x^2+x-1)=(A(x+1)+B(2x-1))/((2x-1)(x+1))`

`(5-x)/(2x^2+x-1)=(Ax+A+2Bx-B)/((2x-1)(x+1))`

`(5-x)/(2x^2+x-1)=(x(A+2B)+A-B)/((2x-1)(x+1))`

`:.(5-x)=x(A+2B)+A-B`

`A+2B=-1`

`A-B=5`

solving the above two linear equations to get A and B ,

subtracting the second equation from the first equation,

`3B=-1-5`

`3B=-6`

`B=-6/3`

B=-2

Plug the value of A in second equation,

`A-(-2)=5`

`A+2=5`

`A=5-2`

A=3

`:.(5-x)/(2x^2+x-1)=3/(2x-1)-2/(x+1)`

## We’ll help your grades soar

Start your 48-hour free trial and unlock all the summaries, Q&A, and analyses you need to get better grades now.

- 30,000+ book summaries
- 20% study tools discount
- Ad-free content
- PDF downloads
- 300,000+ answers
- 5-star customer support

Already a member? Log in here.

Are you a teacher? Sign up now