College Algebra
Given the two functions fff and ggg, find fg\frac{f}{g}gf and identify the domain.
f(x)=5x+2x2−36,g(x)=6x−12x2−36f\left(x\right)=\frac{5x+2}{x^2-36},g\left(x\right)=\frac{6x-12}{x^2-36}f(x)=x2−365x+2,g(x)=x2−366x−12
(fg)(x)=5x+26x−12\left(\frac{f}{g}\right)\left(x\right)=\frac{5x+2}{6x-12}(gf)(x)=6x−125x+2 ,(−∞,−6)∪(−6,2)∪(2,6)∪(6,∞)\left(-\infty,-6\right)\cup\left(-6,2\right)\cup\left(2,6)\cup\left(6,\infty\right)\right.(−∞,−6)∪(−6,2)∪(2,6)∪(6,∞)
(fg)(x)=5x+26x−12\left(\frac{f}{g}\right)\left(x\right)=\frac{5x+2}{6x-12}(gf)(x)=6x−125x+2 ,(−∞,−6)∪(−6,2)\left(-\infty,-6\right)\cup\left(-6,2\right)(−∞,−6)∪(−6,2)
(fg)(x)=6x−125x+2\left(\frac{f}{g}\right)\left(x\right)=\frac{6x-12}{5x+2}(gf)(x)=5x+26x−12 ,(−∞,−6)∪(−6,2)∪(6,∞) \left(-\infty,-6\right)\cup\left(-6,2\right)\cup\left(6,\infty\right) (−∞,−6)∪(−6,2)∪(6,∞)
(fg)(x)=6x−125x+2\left(\frac{f}{g}\right)\left(x\right)=\frac{6x-12}{5x+2}(gf)(x)=5x+26x−12 ,(−∞,−6)∪(6,∞)\left(-\infty,-6\right)\cup\left(6,\infty\right)(−∞,−6)∪(6,∞)