How do you do this Please Explain how you did

Domain : (- ∞, - 5), and (3 / 2, ∞),

Range : (∞, 0.4437]

Step-by-step explanation:

Assuming that we want our answer in interval notation, let's start by determining the domain. Remember that the domain can be found where the function is undefined.

Given : f(x) = (2x - 7) / (2x² + 7x - 15)

Alternative Form : (2x - 7) / (x + 5)(2x - 3)

To receive this 'alternative form' we can simply factor the expression 2x² + 7x - 15. See the procedure below,

Now let's find the domain using the expression '(x + 5)(2x - 3) = 0.' If the denominator equals 0, the function is considered undefined.

Knowing these solutions the domain has the intervals (- ∞, - 5), and (3 / 2, ∞). The range is the set of values that correspond to the domain, so in this case the range would be (∞, 42 + 8√17 / 169]. 42 + 8√17 / 169 = (About) 0.4437, so it lies on the interval (∞, 0.4437].

The images below represent the plotted function in two areas. There are 3 curves in this graph.