how do i solve this equation?

(x+9) / (x-5) + 2x / (5-x)
(x+9) / (x-5) + -2x / (x-5)
(9-x) / (x-5)

= ([x + 9]/[x - 5]) + (2x/[5 - x])
= (x + 9 - 2x)/(x - 5)
= (9 - x)/(x - 5)

Answer: (9 - x)/(x - 5)

you cannot solve this. It is not an eq, just simply the expression

(x+9)/(x-5) - 2x/(x-5)
=(9-x)/(x-5)

((x +9)/(x-5)) plus ((2x)/(5-x))
x+9 (5-x) + 2x(x-5)
5x - x^2 - 9x + 45 + 2x^2 -10x
x^2 -14x + 45
(x-9)(x-5)

(x + 9)/(x - 5) + 2x/(5 - x)
= (x + 9)/(x - 5) - 2x/(x - 5)
= (x + 9 - 2x)/(x - 5)
= (x - 2x + 9)/(x - 5)
= (-x + 9)/(x - 5)

(x+9)/(x-5) + (2x)/(5-x)
=(x-5)(5-x) [(x+9)/(x-5) + (2x)/(5-x)]
=(x+9)(5-x) + (2x)(x-5) / [(x-5)(5-x)]
=(5x+45-x^2-9x+2x^2-10x)/[(x-5)(5-x)]
=(x^2-14x+45)/[(x-5)(5-x)]
=[(x-9)(x-5)]/[(x-5)(5-x)]
=(x-9)/(5-x)

norman is right. you can only simplify

(x+9) (2x) * (-1)
----- + ---------------------
(x-5) (5-x) * (-1)

notice: I'm multiplying the "top" and "bottom" buy -1/-1 = 1 This is allowed!

The expression becomes:

x+9 / x-5 + -2x / x-5

= -x+9 / x-5

notice: the common denominator "common bottom"

(x+9)/x-5) + 2x/(5-x)
(x+9)/(x-5) - 2x/(x-5)
(x+9-2x)/(x-5)
(9-x)/(x-5)

simplify it right?

find the common denominator:
(5-x)((xplus 9)/(x-5)) + (5-x)((2x)/(5-x))
=5xplus45-x^2-9xplus10x-2x^2
simplify that to :(-3x^2 + 6x +45)/((5-x)(x-5)
and you can even factor out the -3 from the top
if you wanna make it look extra sexy haha jk
check my math though yeh?

Ok so your question is:

(x + 9) 2x
---------- + ------
(x - 5) (5 - x)


Well first you find the common denominator, which is:
(5 - x) (x - 5)

That equals:
-x²-25

Now you multiply -x² -25 to the whole equation:


(x + 9) 2x
---------- + ------ (-x² - 25)
(x + 5) (5 - x)

You get:
(x + 9) (5 - x) + 2x (x - 5)

Foil (x + 9) and (5 - x): -x² - 4x + 45

Simplify 2x ( x - 5): 2x² - 10x

Add the two together and your answer is:
x² -14x + 45

If you want it factored it would be:
(x - 9)(x - 5)

I hope that's right. (=