Answer:
[tex]\large\boxed{\dfrac{x^3+6x}{80x+64}}[/tex]
Step-by-step explanation:
[tex]\dfrac{\frac{1}{8}+\frac{x+4}{16}}{\frac{x+4}{x^2}+\frac{4}{x}}=\left(\dfrac{1\cdot2}{8\cdot2}+\dfrac{x+4}{16}\right):\left(\dfrac{x+4}{x^2}+\dfrac{4\cdot x}{x\cdot x}\right)\\\\=\left(\dfrac{2}{16}+\dfrac{x+4}{16}\right):\left(\dfrac{x+4}{x^2}+\dfrac{4x}{x^2}\right)=\dfrac{2+x+4}{16}:\dfrac{x+4+4x}{x^2}\\\\=\dfrac{x+6}{16}:\dfrac{5x+4}{x^2}=\dfrac{x+6}{16}\cdot\dfrac{x^2}{5x+4}=\dfrac{(x+6)(x^2)}{(16)(5x+4)}\\\\\text{use distributive property}\ a(b+c)=ab+ac[/tex]
[tex]=\dfrac{(x)(x^2)+(6)(x)}{(16)(5x)+(16)(4)}=\dfrac{x^3+6x}{80x+64}[/tex]
