Question

Not a physics related question
(2-((x+6)/x))/(8+((x-6)/(x+6)))
equation factored is
(x-6)(x+6)/(3x(3x+14))
I need to know how to get to this answer! Please!

Answer 1

\(\Large 2-\frac{x+6}{x}=\frac{2x-(x+6)}{x}=\frac{x-6}{x}\)

\(\Large 8+\frac{x-6}{x+6}=\frac{8(x+6)+(x-6)}{x+6}=\frac{8x+48+x-6}{x+6}=\frac{9x+42}{x+6}=\frac{3(3x+14)}{x+6}\)

\(\huge \Rightarrow\frac{2-\frac{x+6}{x}}{8+\frac{x-6}{x+6}}=\frac{\frac{x-6}{x}}{\frac{3(3x+14)}{x+6}}=\frac{(x-6)(x+6)}{3x(3x+14)}\)