Chapter SH, Problem 5.5EP

To determine

Find the simplified form of the given expression.

Answer to Problem 5.5EP

The simplified form of the expression is $2x^2{y}^3-5y^4$ .

Explanation of Solution

Given:

The given expression is $\frac{4x^3{y}^4-10x{y}^5}{2xy}$ .

Calculation:

  $\frac{4x^3{y}^4-10x{y}^5}{2xy}$

Use sum of quotients.

  $\frac{4x^3{y}^4}{2xy}-\frac{10x{y}^5}{2xy}$

Divide.

  $\begin{array}{l}=\frac{4}{2}{x}^{3-1}{y}^{4-1}-\frac{10}{2}{x}^{1-1}{y}^{5-1}\\ =2x^2{y}^3-5x^0{y}^4\\ x^0=1\\ =2x^2{y}^3-5y^4\end{array}$

Hence the simplified form of the expression is $2x^2{y}^3-5y^4$ .