Question Number 141663 by ajfour last updated on 22/May/21
$$\:\underset{\:\:−−−−−−−−−−−−−−−−−−−} {\:} \\ $$$$\:\:{x}^{\mathrm{2}} \left({x}−\mathrm{12}\right)\left({x}−\mathrm{15}\right)={k}\left({x}−\mathrm{16}\right) \\ $$$$\:\:\:\:{find}\:{x}\:{in}\:{terms}\:{of}\:{k}\:\left(>\mathrm{0}\right). \\ $$$$\:\:\overset{−−−−−−−−−−−−−−−−−−−} {\:} \\ $$
Commented by Rasheed.Sindhi last updated on 22/May/21
$$\frac{{x}^{\mathrm{2}} \left({x}−\mathrm{12}\right)\left({x}−\mathrm{15}\right)}{{x}−\mathrm{16}}={k} \\ $$$${k}>\mathrm{0}\:\Rightarrow{x}\nleq\mathrm{12}\:\wedge\:\mathrm{15}\nleq{x}\nleq\mathrm{16} \\ $$$$\:\:\:\:\:\:\:\:\:\:\Rightarrow{x}\in\left(\mathrm{12},\mathrm{15}\right)\cup\left(\mathrm{16},\infty\right) \\ $$$$ \\ $$