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Maslowich
2 years ago
14

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

Mathematics
1 answer:
alekssr [168]2 years ago
6 0

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.

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