Question

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

a. (x+5)(x+2)/(x^3-9x)
b. (x+5)(x+4)/(x^3-9x)
c. (-2x+11)/(x^3-12x-9)
d. 3(x+2)/(x^2-3x)

Answer 1

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

Answer 2

Answer: Option A is correct
`((x+2)(x+5))/((x^(3)-9))`

Step-by-step explanation:

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

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

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

after simplifying

we will get
`((2x+5)(x+3)-(3x+5)-x(x+1))/(x(x-3)(x+3))`

After further simplification we will get

`(2x^(2) +11x+15-3x-5-x^(2)-x)/(x( x^(2)-9))`

On more simplification we will get

`(x^(2) +7x+10)/(x(x^(2)-9))`

finally after simplification we will get

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

which will lead to the final result

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