Question

What is the solution to the equation m/m plus 4 plus 4/4-m = m^2/m^2-16?

Answer 1

m= -1

Explanation:

Given:

m/m plus 4 plus 4/4-m = m^2/m^2-16

interpreted as

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

Solution

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

rearrage and expand

-m / ((m+4)(m-4)) = m^2 / ((m+4)(m-4))

if m does not equal 0, we can cancel terms in numerator

-1 / ((m+4)(m-4)) = m / ((m+4)(m-4))

if m does not equal +4 nor -4, we can cancel terms in denomnator

-1 = m

Hence m=-1 if m does not equal 0, -4 or +4, which is valid.