Question

What is the difference?

2x + 5/x 2 - 3x - 3x + 5/x3 - 9x - x + 1/x2 - 9


(x + 5)(x + 2)/x3 - 9x

(x + 5)(x + 4)/x3 - 9x

-2x + 11/x3 - 12x - 9

3(x + 2)/x2 - 3x


Edit: It's A

Answer 1

A

Explanation:

Answer 2

The option
`((x+5)(x+2))/(x^3-9x)` is correct

The difference of the given expression is

`(2x+5)/(x^2-3x)-((3x+5)/(x^3-9x))-({(x+1)/(x^2-9))=((x+5)(x+2))/(x^3-9x)`

Explanation:

Given expression is
`(2x+5)/(x^2-3x)-((3x+5)/(x^3-9x))-({(x+1)/(x^2-9))`

To find the difference of the given expression as below :

`(2x+5)/(x^2-3x)-((3x+5)/(x^3-9x))-({(x+1)/(x^2-9))`

`=(2x+5)/(x(x-3))-((3x+5)/(x(x^2-9)))-({(x+1)/(x^2-9))`

`=(2x+5)/(x(x-3))-((3x+5)/(x(x^2-3^2)))-({(x+1)/(x^2-3^2))`

`=(2x+5)/(x(x-3))-((3x+5)/(x(x-3)(x+3)))-({(x+1)/((x-3)(x+3)))`

( using the formula
`a^2-b^2=(a+b)(a-b)` )

`=(2x+5(x+3)-(3x+5)-x(x+1))/(x(x-3)(x+3))`

`=(2x^2+6x+5x+15-3x-5-x^2-x)/(x(x-3)(x+3))` (adding the like terms)

`=(x^2+7x+10)/(x(x^2-9))` ( by factoring the quadratic polynomial )

`=((x+5)(x+2))/(x^3-9x)`

Therefore
`(2x+5)/(x^2-3x)-((3x+5)/(x^3-9x))-({(x+1)/(x^2-9))=((x+5)(x+2))/(x^3-9x)`

Therefore the difference of the given expression is

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

Therefore option
`((x+5)(x+2))/(x^3-9x)` is correct