Step 1:
Write the original function
[tex]g(x)\text{ = }\frac{-8}{4x^2\text{ + 5x}}[/tex]
Step 2:
Find g(x + 3) by substituting x in original g(x) by x+3
[tex]\begin{gathered} g(x\text{ +3) = }\frac{-8}{4(x+3)^2\text{ + 5(x+3)}} \\ =\text{ }\frac{-8}{4(x^2\text{ + 6x + 9) + 5x + 15}} \\ =\text{ }\frac{-8}{4x^2\text{ + 24x + 36 + 5x + 15}} \\ \text{= }\frac{-8}{4x^2\text{ + 29x + 51}} \end{gathered}[/tex]
Final answer
[tex]g(x\text{ + 3) = }\frac{-8}{4x^2\text{ + 29x + 51}}[/tex]
