Answer:
[tex]\frac{n^{2}-5}{n^{2}-2}[/tex]
Step-by-step explanation:
The rational expression is [tex]\frac{n^{4}-11n^{2}+30}{n^{4}-7n^{2}+10}[/tex]
Now we will simplify numerator first
[tex]n^{4}-11n^{2}+30[/tex]
=[tex]n^{4}-11n^{2}+30=n^{4}-6n^{2}-5n^{2}+30[/tex]
[tex]=n^{2}(n^{2}-6)-5(n^{2}-6)=(n^{2}-5)(n^{2}-6)[/tex]
Now we will simplify the denominator
[tex]n^{4}-7n^{2}+10=n^{4}-5n^{2}-2n^{2}+10[/tex]
[tex]=n^{2}(n^{2}-5)-2(n^{2}-5)=(n^{2}-2)(n^{2}-5)[/tex]
Now the fraction becomes
[tex]\frac{(n^{2}-5)(n^{2}-6)}{(n^{2}-2)(n^{2}-6)}=\frac{n^{2}-5}{n^{2}-2}[/tex]
So the answer is [tex]\frac{n^{2}-5}{n^{2}-2}[/tex]
