Question

How do you simplify `(45a^5b(8-a))/(20a^2b^3(a-8))` and what are the restrictions?

Answer 1

Given `(45a^5b(8-a))/(20a^2b^3(a-8)`

This expression is only defined if the denominator is not equal to zero;
therefore `a!=0, b!=0, a!=8`

`(45a^5b(8-a))/(20a^2b^3(a-8)`

`= color(red)(45/20) * color(green)((a^5)/(a^2)) * color(orange)((b)/(b^3)) * color(blue)((8-a)/(a-8))`

`= color(red)(9/4) * color(green)(a^3) * color(orange)(1/(b^2)) * color(blue)((-1))`

`= - (9a^3)/(4b^2)`