what is the difference?\n$\frac{x}{x^{2}-16}-\frac{3}{x - 4}$\n$\frac{2(x + 6)}{(x + 4)(x…

what is the difference?\n$\frac{x}{x^{2}-16}-\frac{3}{x - 4}$\n$\frac{2(x + 6)}{(x + 4)(x - 4)}$\n$\frac{-2(x + 6)}{(x + 4)(x - 4)}$\n$\frac{x - 3}{(x + 5)(x - 4)}$\n$\frac{-2(x - 6)}{(x + 4)(x - 4)}$

what is the difference?\n$\frac{x}{x^{2}-16}-\frac{3}{x - 4}$\n$\frac{2(x + 6)}{(x + 4)(x - 4)}$\n$\frac{-2(x + 6)}{(x + 4)(x - 4)}$\n$\frac{x - 3}{(x + 5)(x - 4)}$\n$\frac{-2(x - 6)}{(x + 4)(x - 4)}$

Answer

Explanation:

Step1: Factor the denominator

Factor $x^{2}-16$ using the difference - of - squares formula $a^{2}-b^{2}=(a + b)(a - b)$. Here $a=x$ and $b = 4$, so $x^{2}-16=(x + 4)(x - 4)$. The expression becomes $\frac{x}{(x + 4)(x - 4)}-\frac{3}{x - 4}$.

Step2: Find a common denominator

The common denominator of the two fractions is $(x + 4)(x - 4)$. Rewrite $\frac{3}{x - 4}$ with the common denominator: $\frac{3}{x - 4}=\frac{3(x + 4)}{(x + 4)(x - 4)}$.

Step3: Subtract the fractions

$\frac{x}{(x + 4)(x - 4)}-\frac{3(x + 4)}{(x + 4)(x - 4)}=\frac{x-3(x + 4)}{(x + 4)(x - 4)}$.

Step4: Simplify the numerator

Expand $x-3(x + 4)$: $x-3x-12=-2x - 12=-2(x + 6)$. So the result is $\frac{-2(x + 6)}{(x + 4)(x - 4)}$.

Answer:

$\frac{-2(x + 6)}{(x + 4)(x - 4)}$