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# how would I find range of this e.g (6/(2x+3)) for x>0 I will put zero in place of x and find range that is 2 but I don't know it will be greater or less than x?

Apr 5, 2018

The range is $y \in \mathbb{R} - \left\{0\right\}$

#### Explanation:

To find the range, proceed as follows

Let $y = \frac{6}{2 x + 3}$

$y \left(2 x + 3\right) = 6$

$2 x y + 3 y = 6$

$2 x y = 6 - 3 y$

$x = \frac{6 - 3 y}{2 y}$

The denominator is $\ne 0$

Therefore,

$y \ne 0$

The range is $y \in \mathbb{R} - \left\{0\right\}$

graph{6/(2x+3) [-18.02, 18.01, -9.01, 9.01]}