Answer: Option A is correct [tex]\frac{(x+2)(x+5)}{(x^{3}-9)}[/tex]
Explanation:
Given equation[tex]\frac{2x+5}{x^{2} -3x}[/tex][tex] - \frac{3x+5}{x^{3} -9x}[/tex][tex] - \frac{x+1}{x^{2} -9}[/tex]
will become as below after taking out the lcm x(x-3)(x+3)
[tex]\frac{2x+5}{x(x-3)} -\frac{3x+5}{x(x-3)(x+3)} -\frac{x+1}{(x-3)(x+3)}[/tex]
after simplifying
we will get [tex]\frac{(2x+5)(x+3)-(3x+5)-x(x+1)}{x(x-3)(x+3)}[/tex]
After further simplification we will get
[tex]\frac{2x^{2} +11x+15-3x-5-x^{2}-x}{x( x^{2}-9)}[/tex]
On more simplification we will get
[tex]\frac{x^{2} +7x+10}{x(x^{2}-9)}[/tex]
finally after simplification we will get
[tex]\frac{(x+2)(x+5)}{x(x^{2}-9)}[/tex]
which will lead to the final result
[tex]\frac{(x+2)(x+5)}{x^{3}-9x}[/tex]
