The simplified fraction is [tex]{\frac{4x}{(x+3)(1+3x)}[/tex].
Solution:
Given expression is
[tex]$\frac{\frac{4}{x+3}}{\frac{1}{x}+3}[/tex]
Let us first simplify the fraction in denominator.
[tex]$\frac{1}{x}+3 =\frac{1}{x} +\frac{3}{1}[/tex]
To make the denominator same multiply and divide the 2nd term by x.
[tex]$ =\frac{1}{x} +\frac{3x}{x}[/tex]
[tex]$ \frac{1}{x}+3 =\frac{1+3x}{x}[/tex]
Substitute this in the given fraction.
[tex]$\frac{\frac{4}{x+3}}{\frac{1}{x}+3}=\frac{\frac{4}{x+3}}{\frac{1+3x}{x}}[/tex]
[tex]$={\frac{4}{x+3}\times \frac{x}{1+3x}[/tex]
[tex]$={\frac{4x}{(x+3)(1+3x)}[/tex]
Hence the simplified fraction is [tex]{\frac{4x}{(x+3)(1+3x)}[/tex].
