[tex]\boxed{h(x)=\frac{f(x)}{g(x)}=\frac{ 3x+5}{-8x-10}, \ for \ x\neq -\frac{5}{4}}[/tex]
Explanation:
Here we have two functions:
[tex]f(x)= 3x+5 \\ \\ g(x)= -8x-10[/tex]
So we need to find the division of these two functions:
[tex]\frac{f(x)}{g(x)}[/tex]
Let's name this new function as [tex]h(x)[/tex], so:
[tex]h(x)=\frac{f(x)}{g(x)}[/tex]
Substituting our functions:
[tex]h(x)=\frac{f(x)}{g(x)} \\ \\ \\ h(x)=\frac{ 3x+5}{-8x-10} \\ \\ \\ But: \\ \\ -8x-10\neq 0 \\ \\ -8x\neq 10 \\ \\ x\neq -\frac{5}{4}[/tex]
Learn more:
Synthetic division: https://brainly.com/question/12251831
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