Math Help PLEASE!!! thanks!?

Question

put these in simplest form.

Question 1. 5x - 3/x

a. 5x-3/x
b. 5x^2 - 3/x
c. 4x/3
d. 2/x

Question 2. x/x+1 - x+1/ x + 2

Question 3. (2x + 3/x) (x-2/x)

THANKS SO MUCH ;)

Answer 1

QUESTION 1:

It's really hard without parentheses to know what you mean exactly with the questions and the answers.

If you meant (5x - 3) / x, then this is already in lowest form.

If you meant 5x - (3/x), then you would want get the same denominator for both. So multiply the first expression by x over x.
(5x² / x) - (3 / x)

Now you can add them to get:
(5x² - 3)
-----------
..... x

I assume this is answer b. (5x² - 3)/x

QUESTION 2:

Again, I assume this is:
x / (x + 1) - (x - 1) / (x + 2)

In other words:
.... x ..... (x - 1)
-------- - --------
(x + 1) . (x + 2)

Here you need to get a common denominator of (x+1)(x+2). Multiply the first fraction by (x+2)/(x+2):

. x (x + 2) ... (x + 1)
------------- - ----------
(x+1)(x+2) . (x + 2)

And multiply the second fraction by (x+1)/(x+1):

. x (x + 2) ... (x+1)(x+1)
------------- - --------------
(x+1)(x+2) . (x+1)(x+2)

Now you have the same equations in the denominator so subtract the numerator:
. x (x + 2) - [ (x+1)(x+1) ]
---------------------------------
........ ( x + 1 )( x + 2 )

Now expand out the terms in the numerator:
x² + 2x - [ x² + 2x + 1 ]
-----------------------------
..... ( x + 1 )( x + 2 )

Simplify the numerator and cancel terms:
x² + 2x - x² - 2x - 1
-------------------------
.. ( x + 1 )( x + 2 )

.......... -1
--------------------
( x + 1 )( x + 2 )

This is the final answer:
-1 / (x+1)(x+2)

QUESTION 3:

(2x + 3) ... (x - 2)
----------- * ---------
..... x ............ x

Multiply across:
(2x + 3)(x - 2)
-------------------
........ x²

And that's about it. You can multiply the numerator out, but since they are factored, you should leave them like that.

Answer 2

Question 1: Answer is a It's already in simplest form.

Question 2: x/x+1 - x+1/ x + 2
x*x/x(x+1)- (x+1)^2/x(x+1) +2x(x+1)/x(x+1)
= [x^2- x^-2x-1+ 2x^2 +2x]/x(x+1)
=(2x^2 - 1)(x(x+1)

Question 3. (2x + 3/x) (x-2/x)
= (2x^2+3)/x (x^2-2)/x
=(2x^4 +x^2-6)/x^2

Answer 3

so easy!answer 1:b
answer2:-1/(x+1)(x+2)
answer3:(2x^3-4x^2+3x-6)/x^2