Chapter 8.2, Problem 23PPS

To determine

To find: the simplified expression.

Answer to Problem 23PPS

The simplified expression is $\frac{7b\left(4y^{2}z-3x\right)}{105x^3{y}^{4}z}$ .

Explanation of Solution

Given information:

The expression is $\frac{4b}{15x^3{y}^2}-\frac{3b}{35x^2{y}^{4}z}$

Calculation: to find the simplified expression, first take LCM of the denominator and then simplify,

LCM of denominator,

  $\begin{array}{l}15x^3{y}^2=3·5·x·x·x·y·y·y\text{ [factor]}\\ 35x^2{y}^{4}z=5·7·x·x·y·y·y·y·z\text{ [factor]}\\ \text{LCM}=3·5·7·x·x·x·y^4·z\\ \text{LCM}=105x^3{y}^4\text{z [multiply]}\end{array}$

Now, simplify the expression,

  $\begin{array}{l}\frac{4b}{15x^3{y}^2}-\frac{3b}{35x^2{y}^{4}z}=\frac{28b{y}^{2}z-21bx}{105x^3{y}^{4}z}\text{ [LCM of denominator and simplify]}\\ \frac{4b}{15x^3{y}^2}-\frac{3b}{35x^2{y}^{4}z}=\frac{7b\left(4y^{2}z-3x\right)}{105x^3{y}^{4}z}\text{ [simplify]}\end{array}$

Thus, the simplified expression is $\frac{7b\left(4y^{2}z-3x\right)}{105x^3{y}^{4}z}$ .