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17 December, 05:27

What is the simplified form of 3 over 4x plus 3 + 21 over 8 x squared minus 14x minus 15

6 times the quantity 2 x plus 5 end quantity over the quantity 2x minus 5 end quantity times 4 x plus 3

6 over the quantity 4 x plus 3

6 times the quantity x plus 1 end quantity over the quantity 2x minus 5 end quantity times 4 x plus 3

6 times the quantity x plus 1 end quantity over the quantity 2x plus 5 end quantity times 4 x plus 3

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Answers (1)
  1. 17 December, 05:50
    0
    First we have to factorize:

    8 x² - 14 x - 15 = 8 x² - 20 x + 6 x - 15 =

    = 4 x (2 x - 5) + 3 (2 x - 5) =

    = (2 x - 5) (4 x + 3)

    Then we will put it into the equation:

    3 / (4 x + 3) + 21 / (2 x - 5) (4 x + 3) =

    = 3 (2 x - 5) + 21 / (2 x - 5) (4 x + 3) =

    = 6 x - 15 + 21 / (2 x - 5) (4 x + 3) =

    = (6 x + 6) / (2 x - 5) (4 x + 3) =

    = 6 (x + 1) / (2 x - 5) (4 x + 3)

    Answer: C) 6 times the quantity x plus 1 end over the quantity 2 x minus 5 end quantity times 4 x plus 3.
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