(x+6/x^2-7x-18) - (2x/x-9)?

= ([x + 6]/[x² - 7x - 18]) - (2x/[x - 9])
= ([x + 6]/[{x - 9}{x + 2}]) - (2x/[x - 9])
= ([x + 6] - 2x[x + 2])/([x - 9][x + 2])
= (x + 6 - 2x² - 4x)/([x - 9][x + 2])
= (- 2x² - 3x + 6)/([x - 9][x + 2])

Answer: (- 2x² - 3x + 6)/([x - 9][x + 2])

(x + 6)/(x^2 - 7x - 18) - 2x/(x - 9)
= (x + 6)/(x^2 + 2x - 9x - 18) - 2x/(x - 9)
= (x + 6)/[(x + 2)(x - 9)] - 2x/(x - 9)
= (x + 6)/[(x + 2)(x - 9)] - [2x(x + 2)]/[(x + 2)(x - 9)]
= (x + 6)/[(x + 2)(x - 9)] - (2x^2 + 4x)/[(x + 2)(x - 9)]
= (x + 6 - 2x^2 - 4x)/[(x + 2)(x - 9)]
= (-2x^2 - 3x + 6)/[(x + 2)(x - 9)]
= -(2x^2 + 3x - 6)/[(x + 2)(x - 9)]

Should read as :-

( x + 6 ) / ( x^2 - 7 x - 18 ) - 2 x / ( x - 9 )

( x + 6 ) / [ ( x - 9 ) ( x + 2 ) ] - 2 x / ( x - 9 )

( x + 6 ) - 2 x ( x + 2 )
-------------------------------------
( x - 9 ) ( x + 2 )

x + 6 - 2 x^2 - 4 x
------------------------------------
( x - 9 ) ( x + 2 )

- 2 x^2 - 3 x + 6
-----------------------------
( x - 9 ) ( x + 2 )

(x+6/x^2-7x-18) - (2x/x-9) = (x+6)/((x+2)*(x-9)) - 2x/(x-9)
= ((x+6) - 2x*(x+2)) / (x+2)*(x-9)
= (x+6 - 2x^2 - 4x) / (x+2)*(x-9)
= (-2x^2 -3x +6) / (x+2)*(x-9)
= - (2x^ +3x -6) / (x^2 -7x -18)

Good luck...

I will go through this step by step
1. First make the denominator of the first term simple
(x+6)/(x+2)(x-9)-(2x/x-9)

2. make the denominator's common
[(x+6)/(x+2)(x-9)]-[(2x)(x+2)/(x+2)(x-9)]

3. then subtract
(x+6-2x^2-4x)/(x+2)x-9)

4. Simplify numerator to get final answer
(-2x^2-3x+6)/(x+2)(x-9)

you could multiply out the denominator back but I'm not sure if you want that, but that answer would look like this
(-2x^2-3x+6)/(x^2-7x-18)

[(x+6)/(x-9)(x+2) -2x/(x-9)=
=(x+6)-2x^2-4x=
=(-2x^2-3x+6)/(x-9)(x+2)

start by solving quadratic eq

{x + 6 / x^2 - 9x + 2x - 18 }- (2x/x-9)

{ x+ 6 / x ( x - 9 ) + 2( x- 9) } - (2x/x-9)

{ x+6 / (x -9) (x+2)} - (2x/x-9)

take 1/x-9 common

1/ x- 9 { x+6 / (x+2) - 2x}

1/ x- 9 [ { x+ 6 - 2x (x+2)} / x+ 2 ]


1/ x- 9 { (x+ 6 - 2x^2 - 4x ) / x+ 2}

1/ x- 9 { -2x^2 - 3x + 6 / x+ 2}

(-2x^2 - 3x + 6 )/ (x +2)( x- 9 )

yes this one is easy

(x+6)/(x-9)(x+2) -(2x)/(x-9)

multiply the other side by x+2

add and you get with this with a common denominator

x+6 -2x(x+2)/(x-9)(x+2)

x+6-2x^2-4x/(x-9)(x+2)

-2x^2-3x+5/(x-9)(x+2)

(-2x-5)(x-1)/(x-9)(x+2) this is the answer because it is as simplified as possible, you cannot cancel anything else out...

(x + 6)/(x^2 - 7x - 18) - 2x/(x - 9)

x^2 - 7x - 18 = (x - 9)(x + 2)

(x + 6)/(x - 9)(x + 2) - 2x/(x - 9)

(x + 6)/(x - 9)(x + 2) - 2x(x + 2)/(x - 9)(x + 2)

(x + 6)/(x - 9)(x + 2) - (2x^2 + 4x)/(x - 9)(x + 2)

(x + 6 - 2x^2 - 4x)/(x - 9)(x + 2)

(-2x^2 - 3x + 6)/(x - 9)(x + 2)

-(2x^2 + 3x - 6)/(x - 9)(x + 2)