An easy algebra exercise

This is another algebra problem that I came across in one of my statistics blogs.

Show that:

\displaystyle \frac{\beta (\beta+1)}{(\alpha+\beta) (\alpha+\beta+1)}+\frac{2 \alpha \beta}{(\alpha+\beta) (\alpha+\beta+1)}+\frac{\alpha (\alpha+1)}{(\alpha+\beta) (\alpha+\beta+1)}=1

The three fractions on the left hand side are from a probability distribution. Hence the sum is 1. The algebra is not bad and is not difficult to verify.

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