Mathematics, 29.07.2019 22:00 ujusdied5176

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

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Answer from: avahrider1

To factor both numerator and denominator in this rational expression we are going to substitute $n^{2}$ with

; so $n^{2} =x$ and $n ^{4} = x^{2}$ . This way we can rewrite the expression as follows:
$\frac{n^{4}-11n^{2} +30 }{n^{2}-7n^{2} +10 } = \frac{ x^{2} -11x+30}{ x^{2} -7x+10}$
Now we have two much easier to factor expressions of the form $a x^{2} +bx+c$ . For the numerator we need to find two numbers whose product is

(30) and its sum

(-11); those numbers are -5 and -6. (-5)(-6)=30

and

.
Similarly, for the denominator those numbers are -2 and -5. (-2)(-5)=10

and

. Now we can factor both numerator and denominator:
$\frac{ x^{2} -11x+30}{ x^{2} -7x+10} = \frac{(x-6)(x-5)}{(x-2)(x-5)}$
Notice that we have (x-5)

in both numerator and denominator, so we can cancel those out:
$\frac{x-6}{x-2}$
But remember than $x= n^{2}$ , so lets replace that to get back to our original variable:
$\frac{n^{2}-6 }{n^{2}-2 }$
Last but not least, the denominator of rational expression can't be zero, so the only restriction in the variable is $n^{2} -2 \neq 0$
$n^{2} \neq 2$
$n \neq +or- \sqrt{2}$

Answer from: cpcoolestkid4

The simplified expression of the given rational function is $\dfrac{n^2-6}{n^2-2}$ and this can be determined by using the factorization method.

Given :

Rational Expression -- $\dfrac{n^4-11n^2+30}{n^4-7n^2+10}$

The following calculation can be used to evaluate the given expression.

First, factorize the numerator separately.

=n^4-11n^2+30

=n^4 -5n^2-6n^2+30

=n^2(n^2-5)-6(n^2-5)

=(n^2-5)(n^2-6)

Now, factorize the denominator separately.

=n^4-7n^2+10

=n^4-5n^2-2n^2+10

=n^2(n^2-5)-2(n^2-5)

=(n^2-5)(n^2-2)

So, the rational expression becomes:

$\dfrac{n^4-11n^2+30}{n^4-7n^2+10} = \dfrac{(n^2-5)(n^2-6)}{(n^2-5)(n^2-2)}$

$=\dfrac{n^2-6}{n^2-2}$

In the rational function, the denominator never be zero that means:

$n^2-2\neq 0$

$n\neq -\sqrt{2} \; or \; \sqrt{2}$

For more information, refer to the link given below:

link

Answer from: Quest

1. is 4 and 2. is 3

step-by-step explanation:

so if you look at the first one you see that 1 is to 4 and 2 is to 8 and so on, so you can see for every 1 there is a times 4 so if it were 3 then it would be 3*4 and it is 12

for number 2 it is 3 because 1 is to 3 and 2 is to 6 so for every 1 there is 3 so if it were 3 then there would be 3*3 = 9

Answer from: Quest

50- 250 is correct i did that one too

step-by-step explanation:

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

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