Answer:
The correct option is C.
Step-by-step explanation:
The given expression is
\(\frac{\frac{4}{x+3}}{(\frac{1}{x}+3)}\)
\(\frac{\frac{4}{x+3}}{(\frac{1}{x}+3)}=\frac{\frac{4}{x+3}}{\frac{1+3x}{x}}\)
The complex faction can be simplified as
\(\frac{(\frac{a}{b})}{(\frac{c}{d})}=\frac{a}{b}\times \frac{d}{c}\)
\(\frac{\frac{4}{x+3}}{(\frac{1}{x}+3)}=\frac{4}{x+3}\times \frac{x}{1+3x}\)
\(\frac{\frac{4}{x+3}}{(\frac{1}{x}+3)}=\frac{4x}{(x+3)(1+3x)}\)
\(\frac{\frac{4}{x+3}}{(\frac{1}{x}+3)}=\frac{4x}{x(1+3x)+3(1+3x)}\)
\(\frac{\frac{4}{x+3}}{(\frac{1}{x}+3)}=\frac{4x}{x+3x^2+3+9x}\)
\(\frac{\frac{4}{x+3}}{(\frac{1}{x}+3)}=\frac{4x}{3x^2+10x+3}\)
Therefore the correct option is C.
