Question

Simplify 3/a + 6/a^2 - 9/a^3

Answer 1

\[3/a + 6/a^2-9/a^3\]

Answer 2

Put them together with a^3 as a common denominator
\[\frac{3 a^2+6 a-9}{a^3} =\frac{3 \left(a^2+2
a-3\right)}{a^3}

\]
Can you still factor the numerator?

Answer 3

Notice that the numerator can be factored as
3 (-1 + a) (3 + a)
Hence the final nice form is
\[
\frac{3 (a-1) (a+3)}{a^3}
\]