Answer
The solutions are $x=-1$ and $x=3$
Work Step by Step
$\dfrac{x+2}{4x+3}=\dfrac{1}{x}$
Take $4x+3$ to multiply the right side and $x$ to multiply the left side:
$x(x+2)=4x+3$
Evaluate the product on the left side:
$x^{2}+2x=4x+3$
Take all terms to the left side and simplify:
$x^{2}+2x-4x-3=0$
$x^{2}-2x-3=0$
Solve by factoring:
$(x+1)(x-3)=0$
Set both factors equal to $0$ and solve each individual equation for $x$:
$x+1=0$
$x=-1$
$x-3=0$
$x=3$
The solutions are $x=-1$ and $x=3$
