3 years ago

How many

Mathematics

1 answer:

tatiyna3 years ago

7 0

Answer:

Step-by-step explanation:

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A scientist has discovered a new strain of bacteria. The bacteria culture initially contained 1000 bacteria and the bacteria are

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Which expression is equivalent to the expression below? StartFraction m + 3 Over m squared minus 16 EndFraction divided by Start

Kamila [148]

Option B: $\frac{1}{(m-4)(m-3)}$ is the correct answer.

Explanation:

The given expression is $\frac{(\frac{m+3}{m^2-16}) }{(\frac{m^2-9}{m+4} )}$

Simplifying the expression, we have,

$\frac{m+3}{m^{2}-16}\times\frac{m+4}{m^2-9}$

Factor the equations, $m^{2}-16\right$ and $m^{2}-9$ ,we get,

$m^{2}-16\right=m^{2}-4^{2}=(m+4)(m-4)$

$m^{2}-9=m^{2}-3^2=(m+3)(m-3)$

Substituting these factored expressions in the above expression, we have,

$\frac{m+3}{(m+4)(m-4)}\times\frac{m+4}{(m+3)(m-3)}$

Cancelling the common terms $m+3$ and $m+4$ , we get,

$\frac{1}{(m-4)(m-3)}$

Thus, the expression equivalent to $\frac{(\frac{m+3}{m^2-16}) }{(\frac{m^2-9}{m+4} )}$ is $\frac{1}{(m-4)(m-3)}$

Hence, Option B is the correct answer.

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