#### Answer

The solution is $x=\dfrac{3}{5}$

#### Work Step by Step

$\dfrac{4x+3}{4}-\dfrac{2x}{x+1}=x$
Multiply the whole equation by $4(x+1)$:
$4(x+1)\Big(\dfrac{4x+3}{4}-\dfrac{2x}{x+1}=x\Big)$
$(x+1)(4x+3)-2x(4)=4x(x+1)$
Evaluate the indicated operations and simplify the equation:
$4x^{2}+7x+3-8x=4x^{2}+4x$
$4x^{2}+7x+3-8x-4x^{2}-4x=0$
$-5x+3=0$
Solve for $x$:
$-5x=-3$
$x=\dfrac{3}{5}$