Answer:
The value of a can be any real number.
Step-by-step explanation:
The given expression is,
[tex]\frac{a^2m+4m}{a^2+4}[/tex]
Taking m common from the numerator.
[tex]\frac{a^2m+4m}{a^2+4}=\frac{(a^2+4)m}{a^2+4}[/tex]
Cancel out the common factor.
[tex]\frac{a^2m+4m}{a^2+4}=m[/tex]
Therefore the value of a can be any real number.
The given expression is not defined, where the value of the denominator is 0.
[tex]a^2+4=0[/tex]
[tex]a^2=-4[/tex]
[tex]a=\pm\ 2i[/tex]
Therefore the given expression is not defined for complex numbers 2i and -2i.
