Simplify the expression:?

Question

x^2 - 9/ x^2 + 3x

^ = to the power of
/ = over (fraction)

please give explanation

Answer 1

you need to factor

x^2 - 9
-----------
x^2 + 3x

becomes

(x-3)(x+3)
--------------
x(x+3)

(x+3)'s cancel out leaving you with

x-3
----
x

Answer 2

Using basic Algebra that is pretty well reduced to it's simpliest form lacking one thing that is rearranging in descending powers of x.

x^2 +3x - 9/x^2:

The key is in the rules of addition and subtraction of fractions and mixed numbers. The other key is that is an expression not an equation since there is no equal sign.

The way you can prove this thing out is first you have to have a common denominator and all numbers have to be converted to fractions:
Start with x^2 it needs to be converted to a fraction with the same denominator as 9/x^2

to make x^2 a fraction with the same denominator as 9/x^2 we have to multiply both the denimonator and nominator by x^2
Now recall that x^2 as a whole number can also be expressed as x^2/1 without changing it's value.
Also x^2 is understood to mean 1*x^2 1(times) x^2 there is always going to be an understood 1.
given that we multiply x^2/x^2 * (times) x^2/1 which gives us.
When multiplying numbers with exponents you add the exponents:
x^4/x^2

that gives us x^4/x^2 -9/x^2 +3x

now we have to convert 3x to a fraction with x^2 as the denominator: We do it the same way:

3x/1 * x^2/X^2 and that will give us 3x^3/ x^2

Ok plug it into the expression:

x^4/x^2 -9/x^2 + 3x^3/x^2

now add and collect terms:

which gives us:

x^4 - 9 + 3x^3
--------------------
........x^2

rearrange terms:

x^4 + 3x^3 -9
-------------------
.......x^2

now factor using associative rules of addition and subtraction:

We can factor the terms x^4 and 3x^3 by factoring out the x.as much as we can.

that is going to give us:

x^2(x^2 +3x) -9
---------------------
.........x^2

Now that is the same as saying:

x^2(x^2 +3x) .... -9
----------------- ........----
........x^2 .............x^2
Now reduce to lowest term:

you can divlde x^2 into X^2 on first number since it is multipled or a multipler.
that makes your denominator 1.
that gives you in turn:

x^2 +3x - 9/x^2
easier to see like this: Using associative rules because of not being able to show math equations on here I am rearranging to put - 9/x^2 as the first term in the statement. That is only because of Y/A you want it as last term in the expression normally.
Don't forget if there is no sign in front of a number it is understood to be a positive sign or plus sign +.
- 9
---- +x^2 + 3x
x^2
Hope that helps. Don't forget to show your work. That is what I would be looking for if I was your teacher.

Answer 3

(x^2-9) can be written as (x+3)(x-3). (x^2+3x) can be written as x(x+3). The binomial (x+3) is divided away and what is left is (x-3)/x.

Answer 4

multiply by x^2 (each term)
x^4-9+3x^3
(x^4+3x^3-9)/x^2