Question

How do you evaluate `(3a -9i +2ai +6)/(a^2+9) + (3-9i+3i+9)/(9+a^2)`?

Answer 1

`(3a+2ai-15i+18)/(9+a^2)`

Explanation:

The first thing we notice with the two expression here is that the denominators are the same since `a^2+9=9+a^2`.

This means that we can "combine" the two fractions to add the numerators:

`(3a-9i+2ai+6+3-9i+3i+9)/(9+a^2)`

Now, we can combine like terms on the numerator. The like terms have been put in the same color, so you just add/subtract them:

`(3a-color(green)(9i)+2ai+color(red)6+color(red)3-color(green)(9i)+color(green)(3i)+color(red)9)/(9+a^2)`

Rearranging to bring like terms closer together and to make it easier to simplify:

`(3a+2ai-color(green)(9i)-color(green)(9i)+color(green)(3i)+color(red)6+color(red)9+color(red)3)/(9+a^2)`

`(3a+2ai-15i+18)/(9+a^2)`