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Maslowich
4 years ago
15

Simplify the rational expression. State any restrictions on the variable.

Mathematics
1 answer:
ExtremeBDS [4]4 years ago
3 0

we are given

\frac{(n^4-10n^2+24)}{(n^4-9n^2+18)}

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)}

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

n\neq -+ \sqrt{6}

we can simplify it

\frac{(n^4-10n^2+24)}{(n^4-9n^2+18)}=\frac{(n^2-4)}{(n^2-3)}

we know that denominator can not be zero

n^2-3\neq 0

n\neq -+ \sqrt{3}

so, option-B.......Answer

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We can find the QS side that is missing by using the proportions (C) QS/SR = PO/OR.

<h3>What do we mean by proportions?</h3>
  • A proportion is an equation that equalizes two ratios.
  • You could, for instance, write the ratio as follows: 1: 3 in the case of 1 boy and 3 girls (for every one boy there are 3 girls)
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So, a proportion that is used to determine the QS's missing side

(A) QS/OR = PO/SR

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(B) PR/PO = QS/QR

  • Not possible because the order of the lines does not allow for the measurement of line length. QS/SR = PO/OR.

(C) QS/SR = PO/OR

  • Given that the sides and base are both perfectly positioned within the fractions, this ratio can be used to determine the length of line QS.

Therefore, we can find the QS side that is missing by using the proportions (C) QS/SR = PO/OR.

Know more about proportions here:

brainly.com/question/19994681

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