## Algebra: A Combined Approach (4th Edition)

$x=2$
$1+\dfrac{3}{x+1}=\dfrac{x}{x-1}$ 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 $x$: $2x=4$ $x=\dfrac{4}{2}$ $x=2$