Answer:
m = -2
Step-by-step explanation:
[tex]\frac{m}{m+4} + \frac{4}{4-m} = \frac{m^2}{m^2-16}\\\\\frac{m}{m+4} + \frac{4}{-(m-4)} = \frac{m^2}{m^2-16}\\\\[/tex] [tex][ \ ( 4 - m) = - (m -4) \ ][/tex]
[tex]\frac{m}{m+4} + \frac{-4}{(m-4)} = \frac{m^2}{m^2-16}\\\\[/tex] [tex][ \ \frac{a}{-b} = \frac{-a}{b}\ ][/tex]
[tex]\frac{m}{m+4} - \frac{4}{m-4} = \frac{m^2}{m^2-16}\\\\[/tex] [tex][ \ \frac{x}{y} + \frac{-a}{b} = \frac{x}{y} - \frac{a}{b} \ ][/tex]
[tex]\frac{m(m-4)-4(m+4)}{(m-4)(m+4)} = \frac{m^2}{m^2-16}\\\\\frac{m^2 -4m -4m-16}{(m^2-16)} = \frac{m^2}{m^2-16}\\\\[/tex] [tex][ \ T aking \ LCM \ and \ simplifying\ ][/tex]
[tex]m^2 - 8m -16 = m^2[/tex] [tex][ \ \frac{a}{b} = \frac{c}{b} => a = c \ ][/tex]
[tex]m^2 - m^2 - 8m - 16 = 0\\\\0 -8m = 16\\\\-8m = 16 \\\\m = \frac{16}{-8} = -2[/tex]
