Question

How do you simplify `\frac { 15x ^ { 5} - 9x ^ { 4} + 6x ^ { 3} } { - 3x ^ { 2} }`?

Answer 1

See a solution process below:

Explanation:

First, rewrite the expression as:

`(15x^5)/(-3x^2) - (9x^4)/(-3x^2) + (6x^3)/(-3x^2) =>`

`-(15x^5)/(3x^2) - -(9x^4)/(3x^2) + -(6x^3)/(3x^2) =>`

`-(15x^5)/(3x^2) + (9x^4)/(3x^2) - (6x^3)/(3x^2) =>`

`-(5x^5)/x^2 + (3x^4)/x^2 - (2x^3)/x^2`

Now, use these rules of exponents to simplify each of the remaining terms:

`x^color(red)(a)/x^color(blue)(b) = x^(color(red)(a)-color(blue)(b))` and `a^color(red)(1) = a`

`-(5x^color(red)(5))/x^color(blue)(2) + (3x^color(red)(4))/x^color(blue)(2) - (2x^color(red)(3))/x^color(blue)(2) =>`

`-5x^(color(red)(5)-color(blue)(2)) + 3x^(color(red)(4)-color(blue)(2)) - 2x^(color(red)(3)-color(blue)(2)) =>`

`-5x^3 + 3x^2 - 2x^color(red)(1) =>`

`-5x^3 + 3x^2 - 2x`