Question

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

Answer 1

Answer:

$\frac{n^{2}-5}{n^{2}-2}$

Step-by-step explanation:

The rational expression is $\frac{n^{4}-11n^{2}+30}{n^{4}-7n^{2}+10}$

Now we will simplify numerator first

$n^{4}-11n^{2}+30$

=$n^{4}-11n^{2}+30=n^{4}-6n^{2}-5n^{2}+30$

$=n^{2}(n^{2}-6)-5(n^{2}-6)=(n^{2}-5)(n^{2}-6)$

Now we will simplify the denominator

$n^{4}-7n^{2}+10=n^{4}-5n^{2}-2n^{2}+10$

$=n^{2}(n^{2}-5)-2(n^{2}-5)=(n^{2}-2)(n^{2}-5)$

Now the fraction becomes

$\frac{(n^{2}-5)(n^{2}-6)}{(n^{2}-2)(n^{2}-6)}=\frac{n^{2}-5}{n^{2}-2}$

So the answer is $\frac{n^{2}-5}{n^{2}-2}$

Answer 2

N^4 - 11 n² + 30 = ( n² - 6 ) ( n² - 5 )
n^4 - 7 n² + 10 = ( n² - 2 ) ( n² - 5 )
( n² - 6 ) ( n² - 5 ) / ( n² - 2 ) ( n² - 5 )= $\frac{ n^{2} -6}{n ^{2} -2}$