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)