Answer
Domain = $\displaystyle \mathbb{R}\backslash\{-\frac{3}{4}\}$ or $\displaystyle \{x\in \mathbb{R}\ |\ x\neq-\frac{3}{4}\}$
Work Step by Step
The domain of a real function ( a function defined on real numbers)
is the set of numbers for which f(x) is defined.
$f(x)=\displaystyle \frac{2x}{4x+3}$ can be calculated for any real number,
except for those yielding a zero in the denominator.
Here,
$4x+3=0$
$4x=-3$
$x=-\displaystyle \frac{3}{4} \quad $must be excluded from the domain.
Domain = $\displaystyle \mathbb{R}\backslash\{-\frac{3}{4}\}$ or $\displaystyle \{x\in \mathbb{R}\ |\ x\neq-\frac{3}{4}\}$
