(3x-2)/(x-3)(x+1) partial fractions

Expert Answers

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

You need to remember the technique called partial fraction decomposition such that:

(3x-2)/(x-3)(x+1) = a/(x-3) + b/(x+1)

Notice that the numerators are not known yet, hence two variables are assigned.

You may get rid of all denominator multiplying all terms by the common denominator (x-3)(x+1) such that:

3x-2 = a(x+1) + b(x-3)

Opening the brackets yields: 3x-2=ax+a+bx-3b

Group the x terms and the constant terms such that: 3x-2=(a+b)x + (a-3b)

Equating the coefficients of like powers yields:

a+b = 3 => a = 3-b

a - 3b = -2 => 3 - b - 3b = -2 => -4b = -5 => b = 5/4

a = 3 - 5/4 = 7/4

Hence, the original fractions were the following: (3x-2)/(x-3)(x+1) = 7/(4x-12) + 5/(4x+14)

Approved by eNotes Editorial Team
Soaring plane image

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