Question

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

n4-11n2+30 / n4-7n2+10

Answer 1

`(n^(2)-5)/(n^(2)-2)`

Explanation:

The rational expression is
`(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

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

So the answer is
`(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 )=
`( n^(2) -6)/(n ^(2) -2)`