Hello there. To solve this question, we'll have to remember some properties about rational functions.
Given the functions:
[tex]f(x)=3x+2[/tex]
And
[tex]g(x)=-2x-3[/tex]
We have to evaluate
[tex]\left(\dfrac{f}{g}\right)(1)[/tex]
For this, remember that:
[tex]\left(\dfrac{f}{g}\right)(x)=\frac{f(x)}{g(x)},g(x)\text{ not equal to 0}[/tex]
The domain of this function is the entire real line, without the point x such that g(x) = 0.
In this case, we'll have
[tex]\left(\dfrac{f}{g}\right)(x)=\frac{3x+2}{-2x-3}[/tex]
Evaluating it at x = 1, we get
[tex]\left(\dfrac{f}{g}\right)(1)=\frac{3\cdot1+2}{-2\cdot1-3}=\frac{3+2}{-2-3}=\frac{5}{-5}=-1[/tex]
This is the value we've been looking for.
