Exercise (Simple Algebra Fact )

Exercise:

Show that, $\frac{3}{13}-\frac{3}{16}=\frac{3}{13}\times \frac{3}{16}$

Solution: we have $\frac{3}{13}-\frac{3}{16}=\frac{m}{n}-\frac{m}{m+n}=\frac{m\left( m+n \right)-mn}{n\left( m+n \right)}$

$=\frac{{{m}^{2}}+mn-mn}{n\left( m+n \right)}=\frac{{{m}^{2}}}{n\left( m+n \right)}=\frac{m}{n}\times \frac{m}{m+n}=\frac{3}{13}\times \frac{3}{16}$