ANSWER
B. 1/4+x ; where x ≠ -4,0
EXPLANATION
The given expression is:
[tex] \frac{x}{4x + {x}^{2} } [/tex]
This expression is defined if and only if,
[tex](4x + {x}^{2} ) \ne 0[/tex]
[tex]x(4 + x) \ne0[/tex]
[tex]x\ne0 \: or \: x\ne - 4[/tex]
The greatest common factor in the denominator is x.
We factor the greatest common factor is
[tex]\frac{x}{x(4 + x)} [/tex]
Cancel the common factors to ontain;
[tex]\frac{1}{4+ x } [/tex]
The correct choice is B.
