Chapter 6.2, Problem 38PPS

To determine

To find: The simplification for the given expression.

Answer to Problem 38PPS

The simplification for the given expression is $-a^{2}b+a-\frac{2}{a}$ .

Explanation of Solution

Given information:

The given expression is,

  $\left(a^3{b}^2-a^{2}b+2b\right){\left(-ab\right)}^{-1}$

The expression is simplified as,

  $\begin{array}{c}\left(a^3{b}^2-a^{2}b+2b\right){\left(-ab\right)}^{-1}=\frac{a^3{b}^2-a^{2}b+2b}{-ab}\\ =\frac{b\left(a^{3}b-a^2+2\right)}{-ab}\\ =\frac{\left(a^{3}b-a^2+2\right)}{-a}\\ =-a^{2}b+a-\frac{2}{a}\end{array}$

Thus, the simplification for the given expression is $-a^{2}b+a-\frac{2}{a}$ .