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# HELP ME OUT PLEASE SOLVE IT.............Check if I am right or wrong ..Rational Expression

Simplify the given rational expression.( Assume that all denominators are nonzero) I have done it myself ,Just want to be sure if I am right .

2x^2+14x+20
----------------
5x^2-25x-70

---------
5(x-7)

18-2x
------------
x^2-3x-54

------
x+6

36-x^2
--------------
x^2-12x+36

x^3-27
------------
3-x

2x2+14x+20
5x2-25x-70

I will work through, and see if our answers match.
(2x+10)(x+2)
(5x-35)(x+2)

(2x+10)
(5x-35)

2(x+5)
5(x-7)

18-2x
x2-3x-54

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

2
(-x-6)

36-x2
x2-12x+36

(6-x)(6+x)
(-x+6)(-x+6)

(6+x)
(-x+6)

x3-27
3-x

The numerator is the arithmetic of two cubes...
x3-33
The equation for adding two cubes is...
(a + b)(a2 – ab + b2)
a=x
b=-3

(x-3)(x2+3x+9)
(3-x)

If we make both the numerator and denominator negative...
-(x-3)(x2+3x+9)
(x-3)

-(x2+3x+9)

a2 - b2 = (a - b)(a + b)

a2 ± 2ab + b2 = (a ± b)2 = (b ± a)2 = b2 ± 2ab + a2

~~~~~~~~~~

36 - x2
3.) = ------------------ =
36 - 12x + x2

(6 - x)(6 + x)
------------------ =
(6 - x)^2

6 + x
--------
6 - x