Chapter 1.2, Problem 54PPS

To determine

Evaluate the expression $\frac{2a-b^2}{ab}+\frac{c-a}{b^2}$ .

Answer to Problem 54PPS

The value of expression is $\frac{1}{2}$ .

Explanation of Solution

Given:

The values of a, b and c are 8, 4 and 16 respectively.

Calculation:

The expression is evaluated as follows:

  $\begin{array}{l}\Rightarrow \frac{2a-b^2}{ab}+\frac{c-a}{b^2}\\ \Rightarrow \frac{2\left(8\right)-{\left(4\right)}^2}{\left(8\right)\left(4\right)}+\frac{\left(16\right)-\left(8\right)}{{\left(4\right)}^2}\\ \Rightarrow \frac{16-16}{32}+\frac{8}{16}\\ \Rightarrow 0+\frac{\cancel{8}}{\cancel{8}\times 2}\\ \Rightarrow \frac{1}{2}\end{array}$

Thus, the value of expression is $\frac{1}{2}$ .