One possible solution is the polynomial \(W(x) = kx\) where \(k \neq 0\) is a constant.
To show that this is a solution, we can plug this into the equation:
\[ \frac{kx}{k(x+1)} = \frac{x}{x+2} \]
\[ \frac{x}{x+1} = \frac{x}{x+2} \]
\[ x(x+2) = x(x+1) \]
which is true for all real numbers \(x\).
Therefore, the polynomial \(W(x) = kx\) where \(k \neq 0\) is a solution to the equation \(xW(x+1) = (x+2)W(x)\).
Find all non-zero polynomials satisfying the equation: x*W(x+1) = (x+2)*W(x) x ∊ R.
W(x)/W(x+1)=x/(x+2)
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