Question

Simplify the rational expression. state any restrictions on the variable. n^4-10nsq+24/n^4-9nsq+18

Answer 1

Substitution:  n² = t
1 ) t² - 10 t + 24 = t² - 6 t - 4 t + 24 = 
= t ( t - 6 ) - 4 ( t - 6 ) = ( t - 6 ) ( t - 4 ) =
= ( n² - 6 ) ( n² - 4 )
2 ) t² - 9 t + 18 = t² - 6 t - 3 t + 18 =
= t ( t - 6 ) - 3 ( t - 6 ) = ( t - 6 ) ( t - 3 ) = 
= ( n² - 6 ) ( n² - 3 )
The restrictions:  n² ≠ 6,  n² ≠ 3,    n ≠ +/- √6,  n≠ +/-√3
Simplification: