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 \(\frac{n^{2}-5}{n^{2}-2}\)
