Answer:
option A
[tex]\frac{(x+2)(x+5)}{x^{3}-9x }[/tex]
Step-by-step explanation:
Take LCM
[tex]\frac{2x+5}{x(x-3)}-\frac{3x+5}{x(x^{2}-9)}+\frac{x+1}{(x+3)(x-3)}[/tex]
[tex]\frac{2x+5}{x(x-3)}-\frac{3x+5}{x((x+3)(x-3))}+\frac{x+1}{(x+3)(x-3)}[/tex]
[tex]\frac{(2x+5)(x+3)}{x(x+3)(x-3)}-\frac{3x+5}{x((x+3)(x-3))}+\frac{(x+1)(x)}{x(x+3)(x-3)}[/tex]
Now the Denominator is same we can add the numerator
[tex]\frac{(2x^{2}+11x+15)}{x(x+3)(x-3)}-\frac{3x+5}{x((x+3)(x-3))}+\frac{(x^{2}+x)}{x(x+3)(x-3)}[/tex]
[tex]\frac{2x^{2}-x^{2}+11x-3x-x+15-5}{x(x+3)(x-3)}[/tex]
[tex]\frac{x^{2}+7x+10}{x(x+3)(x-3)}[/tex]
[tex]\frac{(x+2)(x+5)}{x(x+3)(x-3)}[/tex]
[tex]\frac{(x+2)(x+5)}{x^{3}-9x}[/tex]
