what is the simplified form of 5/x+7 - 3/x-3?

Using brackets:-
5 / (x + 7) - 3 / (x - 3)

5 (x - 3) - 3(x + 7)
-----------------------
(x + 7)(x - 3)

5x - 15 - 3x - 21
----------------------
(x + 7)(x - 3)

2x - 36
----------------
(x + 7)(x - 3)

2 (x - 18)
-----------------
(x + 7)(x - 3)

2)x^2-2x-24+9=0 x^2-2x-15=0 x^2-5x+3x-15=0 x(x-5)+3(x-5) x=-3,5 3)x^2-x-30=0 x^2-6x+5x-30=0 x(x-6) +5(x-6)=0 x=-5,6

5/(x + 7) - 3/(x - 3)
= 5x - 15 - 3x - 21
= 2x - 36
= 2(x - 18)

5/(x + 7) - 3/(x - 3)

5(x - 3) - 3(x + 7)

5x - 15 - 3x - 21

2x - 36 = 0

2x = 36

x = 18.

and x + 7 dif 0 -> x dif - 7
x - 3 dif 0 -> x dif 3.

S = {x E R / x = 18}.

5/x -3/x = 2/x and 7-3=4 so 2/x+4 equals x+4

x+4

I interpreted it two ways.
1st way
5/x + 7 - 3/x - 3
5/x - 3/x = 2/x
7 - 3 = 4
2/x + 4 This could be an answer.
Or you can combine them further. Find a common denominator which is x
Numerator = 2 + 4x
Denominator = x
This can't be simplified

2nd way.
5/(x+7) - 3/(x-3) First find a common denominator which will be (x+7)(x-3).

Numerator: 5(x-3) - 3(x+7)
5x - 15 - 3x - 21
2x - 36
2(x - 18)

Denominator: (x+7)(x - 3)

This fraction can't be simplified.

well, i added 5/x + 7/1 by finding common denominators then subtracted the 3/x -3/1 by also finding common denominators. i eventually got 4x + 2 all over x but i think you can get rid of the x because it is in both the numerator and denominator...so 6??

if the question reads straight and there are no parenthesis in there.. then the answer is 2/x + 4

you combine the like terms