Question

Which expression is equivalent to the expression below? (m+3/m^2-16)/(m^2-9/m+4)

Answer 1

B. 1/(m-4)(m-3)

Answer 2

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

Explanation:

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

Lets factor the numerator and denominator

use identity a^2 - b^2 = (a+b)(a-b)

`m^2 - 16= m^2 - 4^2 = (m+4)(m-4)`

`m^2 - 9= m^2 - 3^2 = (m+3)(m-3)`

we have divisiion sign in between, change the division symbol in to multiplication symbol by flipping the fraction in the denominator

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

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

Cancel put m+3 and m+4 at the top and botom

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