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Lera25 [3.4K]
3 years ago
12

Simplify the rational expression. state any restrictions on the variable. n^4-11n^2+30/n^4-7n^2+10

Mathematics
1 answer:
Andrej [43]3 years ago
7 0
<span>For this case we have the following expression:
</span> \frac{n ^ 4-11n ^ 2 + 30}{ n ^ 4-7n ^ 2 + 10} &#10;&#10;
<span> We are going to make the following change of variables:
 </span>x = n ^ 2&#10;
 <span>Rewriting the expression we have:
 </span>\frac{(x ^ 2-11x + 30)}{(x ^ 2-7x + 10)} &#10;&#10;
 <span>Factoring the expression we have:
 </span>\frac{(x-5) (x-6)}{(x-5) (x-6)} &#10;
 <span>Canceling similar terms we have:
 </span>\frac{x-6}{x-2} &#10;
 <span>Returning the change we have:
 </span>\frac{n ^ 2-6}{n ^ 2-2} &#10;&#10;
<span> The resctrictions of the function are those that make the denominator equal to zero.
 We have then:
 </span>n ^ 2-2 = 0&#10;&#10;n = +/-  \sqrt{2} &#10;
<span> Answer:
 The simplified expression is:
 </span>\frac{n ^ 2-6}{n ^ 2-2}
 <span>The restrictions are:
 </span>n = \sqrt{2} &#10;
 n = -  \sqrt{2}
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"An angle that forms a linear pair with one of the interior angle the triangle" is the best definition of an exterior angle of a triangle.

<u>Option: C</u>

<u>Explanation:</u>

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In the most easiest pattern , since any angle of triangle equivalent is 60′, the outer angle would be 120′. Therefore all exterior angles sum is:

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-Dominant- [34]

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Step-by-step explanation:

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Nick and eddie are both thinking of a number. Eddies number is 3/7 of nicks number. There is a difference of 52 between their tw
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Answer:

nick's number = 91

eddie's number = 39

Step-by-step explanation:

n = nick's number

\frac{3}{7}n = eddie's number

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cross-multiply:  4n = 52(7)

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eddie's number:  \frac{3}{7} · 91 =  273/7 = 39

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