Question

How do you evaluate `\frac { 15a ^ { 5} - 15a ^ { 4} + 5} { 5a }`?

Answer 1

See a solution process below:

Explanation:

One way to evaluate this expression is to rewrite it as:

`(15a^2)/(5a) - (15a^4)/(5a) + 5/(5a)`

Next, factor common terms out of each fraction giving:

`(color(red)(cancel(color(black)(15)))3color(blue)(cancel(color(black)(a^2)))a)/(color(red)(cancel(color(black)(5)))color(blue)(cancel(color(black)(a)))) - (color(red)(cancel(color(black)(15)))3color(blue)(cancel(color(black)(a^4)))a^3)/(color(red)(cancel(color(black)(5)))color(blue)(cancel(color(black)(a)))) + color(red)(cancel(color(black)(5)))/(color(red)(cancel(color(black)(5)))a) =>`

`3a - 3a^3 + 1/a`

If necessary, the first two terms can also be factored as:

`(3a * 1) - (3a * a^2) + 1/a =>`

`3a(1 - a^2) + 1/a`