first part:
divide out the 12 from numerator

12x+12 = 12(x+1)

divide out 4 from denominator 4x+16 = 4(x+4)

\(\displaystyle{12}\frac{{{x}+{1}}}{{4}}{\left({x}+{4}\right)}={3}\frac{{{x}+{1}}}{{{x}+{4}}}\)

second part: x+4 = x+4, nothing to divide out

\(\displaystyle{4}{x}^{{2}}-{4}={4}{\left({x}^{{2}}-{1}\right)}\) divide out 4 from denominator

4(x^2 - 1) = 4(x+1)(x-1)

multiply first and second parts together: \(\displaystyle{3}\frac{{{x}+{1}}}{{{x}+{4}}}\cdot\frac{{{x}+{4}}}{{4}}{\left({x}+{1}\right)}{\left({x}-{1}\right)}\)

x+4's cancel out

x+1's cancel out

answer: \(\displaystyle\frac{{3}}{{4}}{\left({x}-{1}\right)}\)

12x+12 = 12(x+1)

divide out 4 from denominator 4x+16 = 4(x+4)

\(\displaystyle{12}\frac{{{x}+{1}}}{{4}}{\left({x}+{4}\right)}={3}\frac{{{x}+{1}}}{{{x}+{4}}}\)

second part: x+4 = x+4, nothing to divide out

\(\displaystyle{4}{x}^{{2}}-{4}={4}{\left({x}^{{2}}-{1}\right)}\) divide out 4 from denominator

4(x^2 - 1) = 4(x+1)(x-1)

multiply first and second parts together: \(\displaystyle{3}\frac{{{x}+{1}}}{{{x}+{4}}}\cdot\frac{{{x}+{4}}}{{4}}{\left({x}+{1}\right)}{\left({x}-{1}\right)}\)

x+4's cancel out

x+1's cancel out

answer: \(\displaystyle\frac{{3}}{{4}}{\left({x}-{1}\right)}\)