Question

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

Answer 1

we are asked to simplify the expression m+3/m^2-16/m^2-9/m+4 in this problem. To answer this problem, we group the first the like terms, in this case, the terms 3/m2 and 16/m2. The difference between these two terms -13/m2. Hence, the overall expression is m - 13/m2 - 9/m + 4. 

Answer 2

The given expression is :$\frac{m+3}{m^{2}-16}. /\frac{m^{2-9} }{m+4}$

We can write the expressions in the form of difference of two squares and apply the formula $a^{2}-b^{2}=$ (a+b)(a-b)

Writing it as difference of two squares we have:

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

Converting division sign to multiplication the second fraction flips .Cancelling the common terms in numerator and denominator we have:

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