## Calculus with Applications (10th Edition)

The solution is $x=-\dfrac{59}{6}$
$\dfrac{4}{x-3}-\dfrac{8}{2x+5}+\dfrac{3}{x-3}=0$ 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: $x=-\dfrac{59}{6}$