Answer
The solution is $x=-\dfrac{59}{6}$
Work Step by Step
$\dfrac{4}{x-3}-\dfrac{8}{2x+5}+\dfrac{3}{x-3}=0$
Multiply the whole equation by $(x-3)(2x+5)$:
$(x-3)(2x+5)\Big(\dfrac{4}{x-3}-\dfrac{8}{2x+5}+\dfrac{3}{x-3}=0\Big)$
$4(2x+5)-8(x-3)+3(2x+5)=0$
$8x+20-8x+24+6x+15=0$
Simplify by combining like terms:
$6x+59=0$
Take $59$ to the right side:
$6x=-59$
Take $6$ to divide the right side:
$x=-\dfrac{59}{6}$
