Second lagrange interpolating polynomial f(x) = 1/x

Question

https://i.stack.imgur.com/tD7bn.jpg

I do not understand how these polynomials are equal to each other at all. For example when I calculate the first one, I find 1*(x-2.75)*(x-4)

Answer 1

You may notice that there is an error in the solutions divisor as it states $(2-2.5)(2-4)$ rather than $(2-2.75)(2-4)$.

So it seems that it is only a typo in the picture solution as the 7is missing $$L_0(x)=\frac{(x-2.75)(x-4)}{(2-2.75)(2-4)}=\frac{(x-2.75)(x-4)}{(-0.75)(-2)}=\frac{2}{3}(x-2.75)(x-4)$$