Hi i wanted to help you but i hate math do i am soooooooo sorry
we are given
![\frac{(n^4-10n^2+24)}{(n^4-9n^2+18)}](https://tex.z-dn.net/?f=%20%5Cfrac%7B%28n%5E4-10n%5E2%2B24%29%7D%7B%28n%5E4-9n%5E2%2B18%29%7D%20%20)
Firstly, we will factor numerators and denominators
![\frac{(n^4-10n^2+24)}{(n^4-9n^2+18)}=\frac{(n^2-6)(n^2-4)}{(n^2-3)(n^2-6)}](https://tex.z-dn.net/?f=%20%5Cfrac%7B%28n%5E4-10n%5E2%2B24%29%7D%7B%28n%5E4-9n%5E2%2B18%29%7D%3D%5Cfrac%7B%28n%5E2-6%29%28n%5E2-4%29%7D%7B%28n%5E2-3%29%28n%5E2-6%29%7D%20%20)
we can see that
n^2 -6 is factor on both numerator and denominator
so, it will get cancelled
and n^2 -6 can not be equal to 0
so, one of restriction is
![n^2-6\neq 0](https://tex.z-dn.net/?f=%20n%5E2-6%5Cneq%200%20)
![n\neq -+ \sqrt{6}](https://tex.z-dn.net/?f=%20n%5Cneq%20-%2B%20%5Csqrt%7B6%7D%20%20)
we can simplify it
![\frac{(n^4-10n^2+24)}{(n^4-9n^2+18)}=\frac{(n^2-4)}{(n^2-3)}](https://tex.z-dn.net/?f=%20%5Cfrac%7B%28n%5E4-10n%5E2%2B24%29%7D%7B%28n%5E4-9n%5E2%2B18%29%7D%3D%5Cfrac%7B%28n%5E2-4%29%7D%7B%28n%5E2-3%29%7D%20%20)
we know that denominator can not be zero
![n^2-3\neq 0](https://tex.z-dn.net/?f=%20n%5E2-3%5Cneq%200%20)
![n\neq -+ \sqrt{3}](https://tex.z-dn.net/?f=%20n%5Cneq%20-%2B%20%5Csqrt%7B3%7D%20%20)
so, option-B.......Answer
50% is
![\frac{50}{100}](https://tex.z-dn.net/?f=%20%5Cfrac%7B50%7D%7B100%7D%20)
We have two ways to do this, pick your favor:
either by fractions:
![\frac{5}{8}](https://tex.z-dn.net/?f=%20%5Cfrac%7B5%7D%7B8%7D%20)
÷
![\frac{1}{2}](https://tex.z-dn.net/?f=%20%5Cfrac%7B1%7D%7B2%7D%20)
(
![\frac{50}{100} = \frac{1}{2}](https://tex.z-dn.net/?f=%20%5Cfrac%7B50%7D%7B100%7D%20%3D%20%20%5Cfrac%7B1%7D%7B2%7D%20)
Multiply by the reciprocal of
![\frac{1}{2}](https://tex.z-dn.net/?f=%20%5Cfrac%7B1%7D%7B2%7D%20)
which is 2(flip it)
![\frac{5}{8}](https://tex.z-dn.net/?f=%20%5Cfrac%7B5%7D%7B8%7D%20)
× 2 =
= 1.25
Or change them to decimals:
![\frac{5}{8} = 0.625](https://tex.z-dn.net/?f=%20%5Cfrac%7B5%7D%7B8%7D%20%3D%200.625)
![\frac{50}{100}](https://tex.z-dn.net/?f=%20%5Cfrac%7B50%7D%7B100%7D%20)
= 0.5
0.625 ÷ 0.5
0.5 I 0.625
multiply by 10 to make it easier to divide(it still gives us the same answer)
0.5 × 10 = 5
0.625 × 10 = 6.25
1.25
5 I 6.25
-5
12
-10
25
-25
0
0.625 ÷ 0.5 =
1.25