\(\frac{a}{b}+\frac{-a}{b+1}=\frac{a\left(b+1\right)}{b\left(b+1\right)}+\frac{-ab}{b\left(b+1\right)}=\frac{ab+a}{b\left(b+1\right)}+\frac{-ab}{b\left(b+1\right)}=\frac{a}{b\left(b+1\right)}\)
\(\frac{a}{b}+\frac{-a}{b+1}=\frac{a\left(b+1\right)}{b\left(b+1\right)}+\frac{-ab}{b\left(b+1\right)}=\frac{ab+a-ab}{b\left(b+1\right)}=\frac{a}{b\left(b+1\right)}\)