Answer
The solution set is $\{-1,3\}$.
Work Step by Step
$\frac{x+2}{4x+3}=\frac{1}{x}$
$=x(4x+3)$
Multiply both sides by the lowest common multiple.
$[x(4x+3)]\cdot \frac{x+2}{4x+3}=[x(4x+3)]\cdot \frac{1}{x}$
Simplify.
$x(x+2)=(4x+3)$
Clear the parentheses.
$x^2+2x=4x+3$
Subtract $4x+3$ from both sides.
$x^2+2x-(4x+3)=4x+3-(4x+3)$
Simplify.
$x^2+2x-4x-3=0$
$x^2-2x-3=0$
Factor.
$x^2-3x+x-3=0$
$x(x-3)+1(x-3)=0$
$(x-3)(x+1)=0$
Set each factor equal to zero.
$x-3=0 $ or $x+1=0$
Isolate $x$.
$x=3 $ or $x=-1$.
