Question

Which expression is equivalent to the expression below?

Answer 1

(m+3)*(m+4)/(m2-9)*(m2-16)
(m+3)*(m+4)/(m-3)*(m+3)*(m-4)*(m+4) dividing here

1/(m-3)*(m-4)
option B is correct

Answer 2

Answer: B is correct.

`(1)/((m-4)(m-3))`

Explanation:

Given expression :
`\frac{(m+3)/(m^2-16)} {(m^2-9)/(m+4)}`

First we write expression into division form.

`(m+3)/(m^2-16)/ (m^2-9)/(m+4)`

Change division to multiplication. Expression after division will flip and division sign change to multiply

`(m+3)/(m^2-16)* (m+4)/(m^2-9)` ----------- (A)

Formula:
`a^2-b^2=(a+b)(a-b)`

`\Rightarrow m^2-16=(m+4)(m-4)`-------------------------(B)

`\Rightarrow m^2-9=(m+3)(m-3)`--------------------------(C)

Substitute B and C into A and we get,

`(m+3)/((m+4)(m-4))* (m+4)/((m+3)(m-3))`

Cancel like factor from top and bottom.

Cancel factors are m+3 and m+4 and we get,

`(1)/((m-4)(m-3))`

B is correct.