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)
