Question Number 66769 by John Kaloki Musau last updated on 19/Aug/19
$${simplify} \\ $$$$\frac{{x}+\mathrm{4}}{{x}−\mathrm{4}}−\frac{\mathrm{5}{x}+\mathrm{20}}{{x}^{\mathrm{2}} −\mathrm{16}} \\ $$
Commented by Prithwish sen last updated on 19/Aug/19
$$\frac{\mathrm{x}+\mathrm{4}}{\mathrm{x}−\mathrm{4}}\:−\:\frac{\mathrm{5}\left(\mathrm{x}+\mathrm{4}\right)}{\left(\mathrm{x}−\mathrm{4}\right)\left(\mathrm{x}+\mathrm{4}\right)} \\ $$$$=\frac{\mathrm{x}+\mathrm{4}}{\mathrm{x}−\mathrm{4}}\:−\:\frac{\mathrm{5}}{\mathrm{x}−\mathrm{4}}\:=\:\frac{\mathrm{x}+\mathrm{4}−\mathrm{5}}{\mathrm{x}−\mathrm{4}}\:=\:\frac{\mathrm{x}−\mathrm{1}}{\mathrm{x}−\mathrm{4}} \\ $$
Commented by John Kaloki Musau last updated on 20/Aug/19
thanks
Answered by Mr Jor last updated on 25/Aug/19
$$\frac{\boldsymbol{{x}}+\mathrm{4}}{\boldsymbol{{x}}−\mathrm{4}}−\frac{\mathrm{5}\left(\boldsymbol{{x}}+\mathrm{4}\right)}{\left(\boldsymbol{{x}}−\mathrm{4}\right)\left(\boldsymbol{{x}}+\mathrm{4}\right)} \\ $$$$\frac{\boldsymbol{{x}}+\mathrm{4}}{\boldsymbol{{x}}−\mathrm{4}}−\frac{\mathrm{5}}{\boldsymbol{{x}}−\mathrm{4}}=\frac{\boldsymbol{{x}}+\mathrm{4}−\mathrm{5}}{\boldsymbol{{x}}−\mathrm{4}} \\ $$$$\:\:\:\:\:\:\:\:\:\:=\frac{\boldsymbol{{x}}−\mathrm{1}}{\boldsymbol{{x}}−\mathrm{4}} \\ $$