Answer
$x=2$
Work Step by Step
$1+\dfrac{3}{x+1}=\dfrac{x}{x-1}$
Multiply the whole equation by $(x+1)(x-1)$ to eliminate all denominators:
$(x+1)(x-1)\Big(1+\dfrac{3}{x+1}=\dfrac{x}{x-1}\Big)$
$(x+1)(x-1)+3(x-1)=x(x+1)$
Evaluate the indicated operations:
$x^{2}-1+3x-3=x^{2}+x$
Take all terms to the left side and simplify the equation by combining like terms:
$x^{2}-x^{2}+3x-x-1-3=0$
$2x-4=0$
Solve for $x$:
$2x=4$
$x=\dfrac{4}{2}$
$x=2$
