Help with this algebra!?

x 3x+5
---------- + ------------
5-x x^2-25

The thing is that you should see that x^2-25 us x*x and 5*5. x^2-25 is the same as (x+5)(x-5)

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

Next thing is to spot 5-x needs to be in the right form. So we put the - outside (- = -1 actually) -(x-5). The order of the terms in the paramter doesn't matter since both are poistive now. Before they actually were (+5-x), but now with the - outside we get a similar form as the stuff on the right.

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

So - now that we can see what unifies them we can multiply the different blocks with what they lack. Left block needs to be multiplied with (x+5), and the right block needs to be multiplied with -1.

So - what we do on the blocks must happen both on the upper number and lower number.
x 3x+5
---------- + --------------
-(x-5) (x+5)(x-5)


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


x^2+5x+(-3x-5)
---------------------
-(x+5)(x-5)

And the final calculations give;
x^2+2x-5
----------------
-(x+5)(x-5)

x/(5 - x) + (3x + 5)/(x^2 - 25)
= -x(x + 5)/(5 - x)(x + 5) - (3x + 5)/(5 - x)(x + 5)
= (-x^2 - 5x)/(5 - x)(x + 5) - (3x + 5)/(5 - x)(x + 5)
= (-x^2 - 5x - 3x - 5)/(5 - x)(x + 5)
= (-x^2 - 8x - 5)/(5 - x)(x + 5)

ASSUME you mean :-

x / (5 - x) + (3x + 5) / (x² - 25)

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

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


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

- x² - 5x + 3x + 5
---------------------------
(x - 5)(x + 5)

5 - 2x - x²
----------------
(x - 5)(x + 5)

PS
Present questions CLEARLY !
Brackets MUST be used.

Could you put grouping symbols please? Hard to identify which is which