Chapter 6.2, Problem 14PPS

To determine

To find: The simplification of the given expression.

Answer to Problem 14PPS

The simplification of the given expression is $\left(7g^{2}h+3g-2h^2\right)$ .

Explanation of Solution

Given information:

The given expression is,

  $\frac{7g^3{h}^2+3g^{2}h-2g{h}^3}{gh}$

The expression is simplified as,

  $\begin{array}{c}\frac{7g^3{h}^2+3g^{2}h-2g{h}^3}{gh}=\frac{g\left(7g^2{h}^2+3gh-2h^3\right)}{gh}\\ =\frac{\left(7g^2{h}^2+3gh-2h^3\right)}{h}\\ =\frac{h\left(7g^{2}h+3g-2h^2\right)}{h}\end{array}$

Simplify further,

  $\begin{array}{c}\frac{7g^3{h}^2+3g^{2}h-2g{h}^3}{gh}=\frac{h\left(7g^{2}h+3g-2h^2\right)}{h}\\ =\left(7g^{2}h+3g-2h^2\right)\end{array}$

Thus, the simplification of the given expression is $\left(7g^{2}h+3g-2h^2\right)$ .