Decompose (3x+4)/(x^2 - 1) into A/(x-1) + B/(x+1). What are the values of A and B?

Boost your skills in A Level Further Mathematics Core Pure. Study with flashcards and multiple choice questions, each question is followed by hints and explanations. Get prepared for your exam with confidence!

Multiple Choice

Decompose (3x+4)/(x^2 - 1) into A/(x-1) + B/(x+1). What are the values of A and B?

Explanation:
Partial fraction decomposition expresses the fraction as a sum of simpler fractions, using that x^2 − 1 factors as (x − 1)(x + 1). Set (3x + 4)/(x^2 − 1) = A/(x − 1) + B/(x + 1). Combining the right-hand side gives [A(x + 1) + B(x − 1)]/[(x − 1)(x + 1)]. Matching numerators: (A + B)x + (A − B) = 3x + 4 So A + B = 3 and A − B = 4. Solving, A = 7/2 and B = 3 − A = 3 − 7/2 = −1/2. Check: (7/2)(x + 1) + (−1/2)(x − 1) = 3x + 4, confirming the decomposition. Therefore A = 7/2 and B = −1/2. The other options fail because they do not satisfy both A + B = 3 and A − B = 4.

Partial fraction decomposition expresses the fraction as a sum of simpler fractions, using that x^2 − 1 factors as (x − 1)(x + 1).

Set (3x + 4)/(x^2 − 1) = A/(x − 1) + B/(x + 1). Combining the right-hand side gives [A(x + 1) + B(x − 1)]/[(x − 1)(x + 1)]. Matching numerators:

(A + B)x + (A − B) = 3x + 4

So A + B = 3 and A − B = 4. Solving, A = 7/2 and B = 3 − A = 3 − 7/2 = −1/2.

Check: (7/2)(x + 1) + (−1/2)(x − 1) = 3x + 4, confirming the decomposition.

Therefore A = 7/2 and B = −1/2. The other options fail because they do not satisfy both A + B = 3 and A − B = 4.

More practice questions
Subscribe

Get the latest from Passetra

You can unsubscribe at any time. Read our privacy policy