What is the correct form of the partial fraction decomposition for the expression 7x+18/x^2+9x

Question

What is the correct form of the partial fraction decomposition for the expression 7x+18/x^2+9x

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Euphemia 5 months 2021-08-19T04:04:21+00:00 2 Answers 6 views 0

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    0
    2021-08-19T04:05:27+00:00

    Answer:

    Option-B

    Step-by-step explanation:

    edge

    0
    2021-08-19T04:06:06+00:00

    x ² + 9x = x (x + 9), so the partial fraction decomposition would be

    (7x + 18) / (x ² + 9x) = a/x + b/(x + 9)

    where a, b are some constants. To find them, multiply both sides by x ² + 9x :

    7x + 18 = a (x + 9) + bx

    Solve for a and b :

    7x + 18 = (a + b) x + 9a

    [ a + b = 7

    [ 9a = 18

    →   a = 2, b = 5

    So

    (7x + 18) / (x ² + 9x) = 2/x + 5/(x + 9)

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Giải phương trình 1 ẩn: x + 2 - 2(x + 1) = -x . Hỏi x = ? ( )