Chapter 11.7, Problem 20PPS

To determine

To write: the given expression as a rational expression.

Answer to Problem 20PPS

The rational expression is $\frac{k^2+k-5}{k-2}$ .

Explanation of Solution

Given:

  $\left(k+2\right)+\frac{k-1}{k-2}$

Calculation:

The rational expression is written below.

  $\begin{array}{l}\left(k+2\right)+\frac{k-1}{k-2}\\ =\left(k+2\right)\left(\frac{k-2}{k-2}\right)+\frac{k-1}{k-2}\\ =\frac{k^2+2^2+k-1}{k-2}\\ =\frac{k^2+k-5}{k-2}\end{array}$

Conclusion:

Therefore, the rational expression is $\frac{k^2+k-5}{k-2}$ .