Question

Find g(x+3) Write your answer without parentheses, and simplify as much as possible.

Answer 1

Step 1:

Write the original function

`g(x)\text{ = }\frac{-8}{4x^2\text{ + 5x}}`

Step 2:

Find g(x + 3) by substituting x in original g(x) by x+3

`\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}`

Final answer

`g(x\text{ + 3) = }\frac{-8}{4x^2\text{ + 29x + 51}}`