What is the solution to the equation the fraction with numerator m and denominator m plus 4 plus the fraction with numerator 4 and denominator 4 minus m is equal to the fraction with numerator m squared and denominator m squared minus 16 ?

The denominators require m ≠ 4 and m ≠ −4. Using the common denominator (m + 4)(m − 4), the left side becomes [m(m − 4) − 4(m + 4)]/[(m + 4)(m − 4)] = (m² − 8m − 16)/(m² − 16). Equating numerators gives m² − 8m − 16 = m², so m = −2, which is allowed. The solution is m equal to negative 2.

AI-written and checked against the verified answer.