Question

Solve. 1+4/n=21/n^2.

Answer 1

`1+\cfrac{4}{n}=\cfrac{21}{n^2}\implies \stackrel{\textit{multiplying both sides by }\stackrel{LCD}{n^2}}{n^2\left( 1+\cfrac{4}{n} \right)=n^2\left( \cfrac{21}{n^2}\right)}\implies n^2+4n=21 \\\\\\ n^2+4n-21=0\implies (n+7)(n-3)=0\implies n= \begin{cases} -7\\ 3 \end{cases}`