Question

How do you simplify `(a + 2 a^ 2 + a) /( a + 2 a^ 3)`?

Answer 1

`\frac{2(a+1)}{a^2+1}`

Explanation:

You can sum similar terms in the numerator: `a+2a^2+a = 2a^2+2a`

Once written in this form, you can factor `a` from both numerator and denominator (and an additional `2` from the numerator):

`\frac{2a^2+2a}{2a^3+a} = \frac{2cancel(a)(a+1)}{cancel(a)(a^2+1)} = \frac{2(a+1)}{a^2+1}`