Question

What is the difference? StartFraction 2 x + 5 Over x squared minus 3 x EndFraction minus StartFraction 3 x + 5 Over x cubed minus 9 x EndFraction minus StartFraction x + 1 Over x squared minus 9 EndFraction

Answer 1

The answer's (A) I set a picture of the answer below too

Answer 2

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

Explanation:

The given expression is

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

First, we need to factor each denominator

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

So, the least common factor (LCF) is
`x(x-3)(x+3)`, because they are the factors that repeats.

Now, we diviide the LCF by each denominator, to then multiply it by each numerator.

`((x+3)(2x+5)-3x-5-x(x+1))/(x(x-3)(x+3)) =(2x^(2)+5x+6x+15-3x-5-x^(2)-x )/(x(x-3)(x+3))\\(x^(2)+7x+10)/(x(x-3)(x+3))`

Then, we factor the numerator, to do so, we need to find two numbers which product is 10 and which sum is 7.

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

Therefore, the expression is equivalent to

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