To simplify this expression, we can factor out common terms in each numerator and denominator:
(a-a^3/a^6+a^2) (a^5-a/a^5+a)= (a(1-a^2)/a^2(a^4+1)) (a(a^4-1)/a(a^4+1))= (a(1-a^2)/a^2(a^4+1)) * ((a^5-a)/a(a^5+1))
Now, cancel out common terms in the numerators and denominators:
= (1-a^2)/(a(a^5+1))= (1-a)(1+a)/(a(a^5+1))
Therefore, the simplified expression is:(1-a)(1+a)/(a(a^5+1))
To simplify this expression, we can factor out common terms in each numerator and denominator:
(a-a^3/a^6+a^2) (a^5-a/a^5+a)
= (a(1-a^2)/a^2(a^4+1)) (a(a^4-1)/a(a^4+1))
= (a(1-a^2)/a^2(a^4+1)) * ((a^5-a)/a(a^5+1))
Now, cancel out common terms in the numerators and denominators:
= (1-a^2)/(a(a^5+1))
= (1-a)(1+a)/(a(a^5+1))
Therefore, the simplified expression is:
(1-a)(1+a)/(a(a^5+1))