The rational function \frac{4x-1}{(x+1)(2x-3)} can be expressed as the sum of two partial fractions: \frac{A}{x+1} and

Question

The rational function \frac{4x-1}{(x+1)(2x-3)} can be expressed as the sum of two partial fractions: \frac{A}{x+1} and \frac{B}{2x-3}
Find the value of A-B:
3
1
-3
-1

Thank you!

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Arianna 2 weeks 2021-09-27T16:10:57+00:00 1 Answer 0

Answers ( )

    0
    2021-09-27T16:12:27+00:00

    Answer:

    -1

    Step-by-step explanation:

    (4x − 1) / ((x + 1) (2x − 3)) = A / (x + 1) + B / (2x − 3)

    Combine the right hand side into one fraction by finding the common denominator.

    (A (2x − 3) + B (x + 1)) / ((x + 1) (2x − 3))

    (2Ax − 3A + Bx + B) / ((x + 1) (2x − 3))

    ((2A + B)x + B − 3A) / ((x + 1) (2x − 3))

    Set the numerator of this fraction equal to the numerator of the original fraction.

    4x − 1 = (2A + B)x + B − 3A

    Match the coefficients.

    4 = 2A + B

    -1 = B − 3A

    Solve the system of equations.  Subtracting the second equation from the first:

    5 = 5A

    A = 1

    B = 2

    A − B = -1

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