$X$ is path connected and b$\in$X, show every path in $X$ is homotopic with endpoints fixed to a path passing through $b$
This is the hint in the book: Let $\gamma$ be a path from $x$ to $y$. If $\alpha$ is any path from $x$ to $y$, then the path $\alpha(\alpha^{-1}\gamma)$ passes through $b$, and it's homotopic to $\gamma$ with endpoints fixed.
I don't understand why $\alpha(\alpha^{-1}\gamma)$ has to pass through $b$
Thanks