Chapter 6.1, Problem 54PPS

To determine

To find: The value of the given relation $\left(\frac{h}{fg}\right)\left(-6\right)$ .

Answer to Problem 54PPS

The value of the given relation is $-\frac{49}{108}$ .

Explanation of Solution

Given:

The given functions are

  $\begin{array}{l}f\left(x\right)=x+2\\ g\left(x\right)=-4x+3\\ h\left(x\right)=x^2-2x+1\end{array}$

Calculation:

The value of the given relation is obtained by substituting the values of the given functions in the given relation.

Substitute the values,

  $\left(\frac{h}{fg}\right)\left(-6\right)$

  $\begin{array}{l}\left(\frac{x^2-2x+1}{\left(x+2\right)\left(-4x+3\right)}\right)\left(-6\right)\\ =\frac{{\left(-6\right)}^2-2\times \left(-6\right)+1}{\left(-6+2\right)\left(-4\left(-6\right)+3\right)}\\ =\frac{36+12+1}{\left(-4\right)\left(27\right)}\\ =-\frac{49}{108}\end{array}$

Therefore, the value of the given relation is $-\frac{49}{108}$ .