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Show that the equation (1) divided by (x+1) - (x)divided by (x-2)=0 has no real roots

Well, to begin, start with 1/(x+1-x). The x's cancel out because they are opposite signs, so now you have 1/1, or just 1. Then, you are dividing 1 by (x-2). In order for an expression to have roots, you have to be able to plug in the roots for x and get 0 out of the equation. In this equation, you might think that 2 is a root. However, that would make the denominator of the fraction 0, which makes the equation undefined. The only way for an equation that's a fraction to have roots is if the numerator = 0. There is no way to get that if the numerator is 1.

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