Question

What is the difference? (2x+5)/(x^2-3x)-(3x+5)/x^3-9x)- (x+1)/x^2-9)

Answer 1

Answer: Option A is correct  $\frac{(x+2)(x+5)}{(x^{3}-9)}$

Explanation:

Given equation$\frac{2x+5}{x^{2} -3x}$$- \frac{3x+5}{x^{3} -9x}$$- \frac{x+1}{x^{2} -9}$

will become as below after taking out the lcm x(x-3)(x+3)

$\frac{2x+5}{x(x-3)} -\frac{3x+5}{x(x-3)(x+3)} -\frac{x+1}{(x-3)(x+3)}$

after simplifying

we will get $\frac{(2x+5)(x+3)-(3x+5)-x(x+1)}{x(x-3)(x+3)}$

After further simplification we will get

$\frac{2x^{2} +11x+15-3x-5-x^{2}-x}{x( x^{2}-9)}$

On more simplification we will get

$\frac{x^{2} +7x+10}{x(x^{2}-9)}$

finally after simplification we will get

$\frac{(x+2)(x+5)}{x(x^{2}-9)}$

which will lead to the final result

$\frac{(x+2)(x+5)}{x^{3}-9x}$

Answer 2

A)(x+5)(x+2)/(x^3-9x)