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)

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)