Question

Simplify the complex fraction.

Answer 1

The simplified fraction is
`{(4x)/((x+3)(1+3x))`.

Solution:

Given expression is

`$((4)/(x+3))/((1)/(x)+3)`

Let us first simplify the fraction in denominator.

`$(1)/(x)+3 =(1)/(x) +(3)/(1)`

To make the denominator same multiply and divide the 2nd term by x.

`$ =(1)/(x) +(3x)/(x)`

`$ (1)/(x)+3 =(1+3x)/(x)`

Substitute this in the given fraction.

`$((4)/(x+3))/((1)/(x)+3)=((4)/(x+3))/((1+3x)/(x))`

`$={(4)/(x+3)* (x)/(1+3x)`

`$={(4x)/((x+3)(1+3x))`

Hence the simplified fraction is
`{(4x)/((x+3)(1+3x))`.