Maths

aⁿ⁺⁴ - a³ⁿ
___________a³ⁿ⁺³ - aⁿ⁺⁷

=
- (a³ⁿ - aⁿ⁺⁴)
_______________ a³ⁿ a³ - aⁿ⁺⁴a³
=
- (a³ⁿ - aⁿ⁺⁴)
______________ a³ (a³ⁿ - aⁿ⁺⁴)

= - 1 / a³ or - a⁻³

2011-10-16 20:28:33 補充：
Use the formula a^(m+n) = a^m * a^n to take out the common factor ,

For example in this question :

a^(n+4) - a^3n
= a^n * a^4 - (a^n)^3
= a^n (a^4 - a^2n)

,

a^(3n+3) - a^(n+7)
= a^n (a^2n+3) - a^n(a^7)
= a^n (a^2n * a^3) - a^n(a^4 * a^3)
= a^n a^3 (a^2n - a^4)

so we can 約分!