Chapter 1.4, Problem 27PPE

To determine

To Evaluate: The expression ${\left(\frac{a}{b}\right)}^2-\frac{c}{a-b}$

Answer to Problem 27PPE

  ${\left(\frac{a}{b}\right)}^2-\frac{c}{a-b}=0$

Explanation of Solution

Given information:

The expression ${\left(\frac{a}{b}\right)}^2-\frac{c}{a-b}$ and value of $a=8,b=4\&c=16$

Concept and Formula Used:

Rule of exponent and addition and subtraction.

  $a^n=a\times a\times a\times \mathrm{..................}n\text{ times}\text{.}$

BODMAS rule

Calculation:

The given expression is ${\left(\frac{a}{b}\right)}^2-\frac{c}{a-b}$

Putting the values of $a=8,b=4\&c=16$ in the expression

  $\begin{array}{l}{\left(\frac{a}{b}\right)}^2-\frac{c}{a-b}={\left(\frac{8}{4}\right)}^2-\frac{16}{8-4}\\ \text{Divide 8 by 4 in side the grouping}\\ {\left(\frac{a}{b}\right)}^2-\frac{c}{a-b}={\left(2\right)}^2-\frac{16}{8-4}\\ \text{Evaluate the power }\\ {\left(\frac{a}{b}\right)}^2-\frac{c}{a-b}=4-\frac{16}{8-4}\\ \text{Subtract 4 from 8 in the denominator of second term}\\ {\left(\frac{a}{b}\right)}^2-\frac{c}{a-b}=4-\frac{16}{4}\\ \text{Divide 16 by 4}\\ {\left(\frac{a}{b}\right)}^2-\frac{c}{a-b}=4-4\\ \text{Simplify}\\ {\left(\frac{a}{b}\right)}^2-\frac{c}{a-b}=0\end{array}$

Conclusion:

  ${\left(\frac{a}{b}\right)}^2-\frac{c}{a-b}=0$