Question

2³+2²+2÷2²+2+1=2 prove that this relation is true for any natural numbers

Answer 1

So, this question is basically asking us "If we had an x instead of a 2, would this be true?" We can try and see what we get:

$\frac{x^3+x^2+x}{x^2+x+1}=x$

So, if we want to show this we have to change the numerator or denominator in such a way that we can cancel some common factors. Notice that $x^3+x^2+x=x(x^2+x+1)$

If we replace the factored numerator with the original one, we get:

$\frac{x(x^2+x+1)}{x^2+x+1}=x \implies \\ x=x$

Since we have an equality, this relation is proved.