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

$x=\dfrac{9}{7}$
$\dfrac{x-3}{x+1}-\dfrac{x-6}{x+5}=0$ Multiply the whole equation by $(x+1)(x+5)$: $(x+1)(x+5)\Big(\dfrac{x-3}{x+1}-\dfrac{x-6}{x+5}=0\Big)$ $(x-3)(x+5)-(x-6)(x+1)=0$ Evaluate both products: $x^{2}+2x-15-x^{2}+5x+6=0$ Simplify the equation by combining like terms: $7x-9=0$ Solve for $x$: $7x=9$ $x=\dfrac{9}{7}$ The original equation is not undefined for this value of $x$, so the solution to this equation is $x=\dfrac{9}{7}$