`(x + 1)/(x^2 - x - 6)` Write the partial fraction decomposition of the rational expression. Check your result algebraically.

Expert Answers

An illustration of the letter 'A' in a speech bubbles


Let's factorize the denominator,





Now let`(x+1)/(x^2-x-6)=A/(x-3)+B/(x+2)`





Equating the coefficients of the like terms,



Now let's solve the above two equations to get the values of A and B,

express B in terms of A from the first equation,


substitute the expression of B in the second equation,







Plug the value of A in the first equation,





Now let's check the above result,








Hence it is verified.

Approved by eNotes Editorial Team

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
Start your 48-Hour Free Trial