# (12x+12)/(4x+16)=

Question
Equations
$$\displaystyle\frac{{{12}{x}+{12}}}{{{4}{x}+{16}}}=$$

2021-03-05
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: $$\displaystyle\frac{{3}}{{4}}{\left({x}-{1}\right)}$$

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