#### Answer

$x=\dfrac{9}{7}$

#### Work Step by Step

$\dfrac{x-3}{x+1}-\dfrac{x-6}{x+5}=0$
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 $x=\dfrac{9}{7}$