Question

Which expression is equivalent to the expression below? StartFraction m + 3 Over m squared minus 16 EndFraction divided by StartFraction m squared minus 9 Over m + 4 EndFraction StartFraction 1 Over (m + 4) (m + 3) EndFraction StartFraction 1 Over (m minus 4) (m minus 3) EndFraction StartFraction m minus 4 Over m minus 3 EndFraction StartFraction m + 3 Over m + 4 EndFraction

Answer 1

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.

Answer 2

Answer:

B. m =6

Step-by-step explanation:

What is the solution to the equation StartFraction 3 Over m + 3 EndFraction minus StartFraction m Over 3 minus m EndFraction = StartFraction m squared + 9 Over m squared minus 9 EndFraction?

m = 3

m = 6

all real numbers

no solution