[ Answer ]
![\boxed{9 * 4 - (2 * 6) \ > \ 2(9-6)}](https://tex.z-dn.net/?f=%5Cboxed%7B9%20%2A%204%20-%20%282%20%2A%206%29%20%5C%20%3E%20%5C%202%289-6%29%7D)
[ Explanation ]
9 * 4 - 2x ___ 2(9 - x)
X = 6
Insert Numbers Into Equation
9 * 4 - (2 * 6) ___ 2(9 - 6)
Solve
9 * 4 = 36
2 * 6 = 12
36 - 12 = 24
9 - 6 = 3
2 * 3 = 6
24 > 6
![\boxed{[ \ Eclipsed \ ]}](https://tex.z-dn.net/?f=%5Cboxed%7B%5B%20%5C%20Eclipsed%20%5C%20%5D%7D)
To factor both numerator and denominator in this rational expression we are going to substitute
![n^{2}](https://tex.z-dn.net/?f=n%5E%7B2%7D%20)
with
![x](https://tex.z-dn.net/?f=%20x%20)
; so
![n^{2} =x](https://tex.z-dn.net/?f=n%5E%7B2%7D%20%3Dx)
and
![n ^{4} = x^{2}](https://tex.z-dn.net/?f=n%20%5E%7B4%7D%20%3D%20%20x%5E%7B2%7D%20%20)
. This way we can rewrite the expression as follows:
![\frac{n^{4}-11n^{2} +30 }{n^{2}-7n^{2} +10 } = \frac{ x^{2} -11x+30}{ x^{2} -7x+10}](https://tex.z-dn.net/?f=%20%5Cfrac%7Bn%5E%7B4%7D-11n%5E%7B2%7D%20%2B30%20%7D%7Bn%5E%7B2%7D-7n%5E%7B2%7D%20%2B10%20%7D%20%3D%20%20%5Cfrac%7B%20x%5E%7B2%7D%20-11x%2B30%7D%7B%20x%5E%7B2%7D%20-7x%2B10%7D%20)
Now we have two much easier to factor expressions of the form
![a x^{2} +bx+c](https://tex.z-dn.net/?f=a%20x%5E%7B2%7D%20%2Bbx%2Bc)
. For the numerator we need to find two numbers whose product is
![c](https://tex.z-dn.net/?f=c)
(30) and its sum
![b](https://tex.z-dn.net/?f=b)
(-11); those numbers are -5 and -6.
![(-5)(-6)=30](https://tex.z-dn.net/?f=%28-5%29%28-6%29%3D30)
and
![-5-6=-11](https://tex.z-dn.net/?f=-5-6%3D-11)
.
Similarly, for the denominator those numbers are -2 and -5.
![(-2)(-5)=10](https://tex.z-dn.net/?f=%28-2%29%28-5%29%3D10)
and
![-2-5=-7](https://tex.z-dn.net/?f=-2-5%3D-7)
. Now we can factor both numerator and denominator:
![\frac{ x^{2} -11x+30}{ x^{2} -7x+10} = \frac{(x-6)(x-5)}{(x-2)(x-5)}](https://tex.z-dn.net/?f=%20%5Cfrac%7B%20x%5E%7B2%7D%20-11x%2B30%7D%7B%20x%5E%7B2%7D%20-7x%2B10%7D%20%3D%20%5Cfrac%7B%28x-6%29%28x-5%29%7D%7B%28x-2%29%28x-5%29%7D%20)
Notice that we have
![(x-5)](https://tex.z-dn.net/?f=%28x-5%29)
in both numerator and denominator, so we can cancel those out:
![\frac{x-6}{x-2}](https://tex.z-dn.net/?f=%20%5Cfrac%7Bx-6%7D%7Bx-2%7D%20)
But remember than
![x= n^{2}](https://tex.z-dn.net/?f=x%3D%20n%5E%7B2%7D%20)
, so lets replace that to get back to our original variable:
![\frac{n^{2}-6 }{n^{2}-2 }](https://tex.z-dn.net/?f=%20%5Cfrac%7Bn%5E%7B2%7D-6%20%7D%7Bn%5E%7B2%7D-2%20%7D%20)
Last but not least, the denominator of rational expression can't be zero, so the only restriction in the variable is
![n^{2} -2 \neq 0](https://tex.z-dn.net/?f=n%5E%7B2%7D%20-2%20%5Cneq%200)
![n^{2} \neq 2](https://tex.z-dn.net/?f=%20n%5E%7B2%7D%20%20%5Cneq%202)