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28 October, 11:44

What is the difference?

x/x^2-16 - 3/x-4

2 (x+6)

(x+4) (x-4)

-2 (x+6)

(x+4) (x-4)

X-3

(x+5) (x-4)

-2 (x-6)

(x+4) (x-4)

+4
Answers (1)
  1. 28 October, 12:37
    0
    Difference is - 2 (x+6) / (x+4) (x-4)

    Step-by-step explanation:

    Step 1:

    Find the difference between x/x²-16 and 3/x-4

    Now x² - 16 = (x-4) (x+4) (using the identity a² - b² = (a+b) (a-b)

    ⇒ x/x²-16 = x / (x-4) (x+4)

    ⇒ x / (x-4) (x+4) - 3/x-4 (Subtracting the both to find difference)

    = 1 / (x-4) [x/x+4 - 3] (Taking the common factor 1/x-4)

    = 1/x-4[x - 3 (x+4) / x+4]

    = 1 / (x-4) (x+4) [x - 3x - 12]

    = 1 / (x-4) (x+4) [-2x - 12]

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