Question

Consider this expression. x-4/2(x+4)

Answer 1

Answer:

Option A

Step-by-step explanation:

We will simplify the expressions given in the options first,

x² - 16 = (x - 4)(x + 4)

2x + 8 = 2(x + 4)

x² + 8x + 16 = (x + 4)²

Option A

$\frac{x^2-16}{2x+8}$ × $\frac{x+4}{x^2+8x+16}$

= $\frac{(x+4)(x-4)}{2(x+4)}\times \frac{(x+4)}{(x+4)^2}$

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

Option B

$\frac{2x+8}{x^2-16}$ ÷ $\frac{x^2+8x+16}{x+4}$

= $\frac{2(x+4)}{(x+4)(x-4)}$ ÷ $\frac{(x+4)^2}{(x+4)}$

= $\frac{2}{(x-4)}\times \frac{1}{(x+4)}$

= $\frac{2}{x^2-16}$

Option C

$\frac{x^2-16}{2x+8}$ ÷ $\frac{x+4}{x^{2}+4x+16}$

= $\frac{(x-4)(x+4)}{2(x+4)}\times \frac{(x+4)^2}{(x+4)}$

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

Option D

$\frac{2x+8}{x^2-16}\times \frac{x^2+8x+16}{x+4}$

= $\frac{2(x+4)}{(x-4)(x+4)}\times \frac{(x+4)^2}{(x+4)}$

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

Therefore, Option A is the answer.