# What is the range of the function  y=(x+5)/(x-2)?

Dec 24, 2016

$\left(- \infty , 1\right) \left(1 , \infty\right)$

#### Explanation:

Solve for $x$, as follows

$y \left(x - 2\right) = x + 5$

$y x - x = 2 y + 5$

$x \left(y - 1\right) = 2 y + 5$

$x = \frac{2 y + 5}{y - 1}$

In the above expression, $x$ becomes undefined for $y = 1$. This except for $y = 1$, $x$ is defined on all the number line. Hence Range of $y$ is $\left(- \infty , 1\right) U \left(1 , \infty\right)$