How do you write the mixed expression (k+2)+(k-1)/(k-2) as a rational expression?

Jun 15, 2017

$\frac{{k}^{2} + k - 5}{k - 2}$

Explanation:

Multiply k+2 by the common denominator (k-2)/(k-2) and then simplify:

$\left(k + 2\right) + \frac{k - 1}{k - 2}$

$= \frac{\left(k + 2\right) \left(k - 2\right)}{k - 2} + \frac{k - 1}{k - 2}$

$= \frac{{k}^{2} - 4}{k - 2} + \frac{k - 1}{k - 2}$

$= \frac{\left({k}^{2} - 4\right) + \left(k - 1\right)}{k - 2}$

$= \frac{{k}^{2} + k - 5}{k - 2}$